Ratio and Proportion Maths Problem Solving












0












$begingroup$


A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $frac{4}{5}$ of the cookies.
The weight of the jar and cookies is now 400g.
How much does the jar weigh?
How many cookies were there from the start?



What I did:
$frac{700}{5}$ = 140



700 - 140 = 560



560 - 400 = 160



But I don't know what to do next.



Thank You and Help is appreciated






algebra-precalculus problem-solving word-problem ratio







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
    $endgroup$
    – Paul
    Sep 29 '18 at 7:48








  • 1




    $begingroup$
    $x$ + $y$ = 700
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:52






  • 1




    $begingroup$
    Ohh wait is it 1/5
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:58






  • 2




    $begingroup$
    Using simultaneous equations I found out that x = 325 so the jar weighs 325g
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 8:27






  • 1




    $begingroup$
    Just a poorly worded question. There are 375g of cookies.
    $endgroup$
    – Paul
    Sep 29 '18 at 12:08
















0












$begingroup$


A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $frac{4}{5}$ of the cookies.
The weight of the jar and cookies is now 400g.
How much does the jar weigh?
How many cookies were there from the start?



What I did:
$frac{700}{5}$ = 140



700 - 140 = 560



560 - 400 = 160



But I don't know what to do next.



Thank You and Help is appreciated






algebra-precalculus problem-solving word-problem ratio







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
    $endgroup$
    – Paul
    Sep 29 '18 at 7:48








  • 1




    $begingroup$
    $x$ + $y$ = 700
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:52






  • 1




    $begingroup$
    Ohh wait is it 1/5
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:58






  • 2




    $begingroup$
    Using simultaneous equations I found out that x = 325 so the jar weighs 325g
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 8:27






  • 1




    $begingroup$
    Just a poorly worded question. There are 375g of cookies.
    $endgroup$
    – Paul
    Sep 29 '18 at 12:08














0












0








0





$begingroup$


A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $frac{4}{5}$ of the cookies.
The weight of the jar and cookies is now 400g.
How much does the jar weigh?
How many cookies were there from the start?



What I did:
$frac{700}{5}$ = 140



700 - 140 = 560



560 - 400 = 160



But I don't know what to do next.



Thank You and Help is appreciated






algebra-precalculus problem-solving word-problem ratio







share|cite|improve this question











$endgroup$




A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $frac{4}{5}$ of the cookies.
The weight of the jar and cookies is now 400g.
How much does the jar weigh?
How many cookies were there from the start?



What I did:
$frac{700}{5}$ = 140



700 - 140 = 560



560 - 400 = 160



But I don't know what to do next.



Thank You and Help is appreciated






algebra-precalculus problem-solving word-problem ratio




algebra-precalculus problem-solving word-problem ratio






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 29 '18 at 7:46









N. F. Taussig

45.1k103358




45.1k103358










asked Sep 29 '18 at 7:43









xx_Gcsemathstudent_xxxx_Gcsemathstudent_xx

406




406








  • 1




    $begingroup$
    Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
    $endgroup$
    – Paul
    Sep 29 '18 at 7:48








  • 1




    $begingroup$
    $x$ + $y$ = 700
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:52






  • 1




    $begingroup$
    Ohh wait is it 1/5
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:58






  • 2




    $begingroup$
    Using simultaneous equations I found out that x = 325 so the jar weighs 325g
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 8:27






  • 1




    $begingroup$
    Just a poorly worded question. There are 375g of cookies.
    $endgroup$
    – Paul
    Sep 29 '18 at 12:08














  • 1




    $begingroup$
    Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
    $endgroup$
    – Paul
    Sep 29 '18 at 7:48








  • 1




    $begingroup$
    $x$ + $y$ = 700
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:52






  • 1




    $begingroup$
    Ohh wait is it 1/5
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 7:58






  • 2




    $begingroup$
    Using simultaneous equations I found out that x = 325 so the jar weighs 325g
    $endgroup$
    – xx_Gcsemathstudent_xx
    Sep 29 '18 at 8:27






  • 1




    $begingroup$
    Just a poorly worded question. There are 375g of cookies.
    $endgroup$
    – Paul
    Sep 29 '18 at 12:08








1




1




$begingroup$
Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
$endgroup$
– Paul
Sep 29 '18 at 7:48






$begingroup$
Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y?
$endgroup$
– Paul
Sep 29 '18 at 7:48






1




1




$begingroup$
$x$ + $y$ = 700
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 7:52




$begingroup$
$x$ + $y$ = 700
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 7:52




1




1




$begingroup$
Ohh wait is it 1/5
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 7:58




$begingroup$
Ohh wait is it 1/5
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 7:58




2




2




$begingroup$
Using simultaneous equations I found out that x = 325 so the jar weighs 325g
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 8:27




$begingroup$
Using simultaneous equations I found out that x = 325 so the jar weighs 325g
$endgroup$
– xx_Gcsemathstudent_xx
Sep 29 '18 at 8:27




1




1




$begingroup$
Just a poorly worded question. There are 375g of cookies.
$endgroup$
– Paul
Sep 29 '18 at 12:08




$begingroup$
Just a poorly worded question. There are 375g of cookies.
$endgroup$
– Paul
Sep 29 '18 at 12:08










2 Answers
2






active

oldest

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1












$begingroup$

You should assign letters to the unknown quantities and form simultaneous equations from them.



I would let the jar's weight be $J$ and the total weight of the cookies be $C$.



The first statement tells you:



$$J+C=700tag 1$$



Then Meghan eats $frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:



$$J +frac15 C = 400 tag 2$$



You now have a pair of simultaneous equations. Im sure you know how to continue this.






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let





    • $j$ - weight of jar


    • $n$ - number of cookies at the beginning


    • $c$ - weight of one cookie


    Then you have
    begin{eqnarray}
    j + ncdot c & = & 700 \
    j + frac{n}{5}cdot c & = & 400
    end{eqnarray}
    $$Rightarrow frac{4}{5}cdot ncdot c = 300$$
    $$Rightarrow ncdot c = frac{5}{4}cdot 300 = 375 = 3cdot 5^3$$



    Restricting our consideration to integers you may have at the beginning, for example:





    • $125$ cookies $3g$ each


    • $25$ cookies $15g$ each


    • $15$ cookies $25g$ each

    • etc.






    share|cite|improve this answer









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      2 Answers
      2






      active

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      2 Answers
      2






      active

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      active

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      active

      oldest

      votes









      1












      $begingroup$

      You should assign letters to the unknown quantities and form simultaneous equations from them.



      I would let the jar's weight be $J$ and the total weight of the cookies be $C$.



      The first statement tells you:



      $$J+C=700tag 1$$



      Then Meghan eats $frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:



      $$J +frac15 C = 400 tag 2$$



      You now have a pair of simultaneous equations. Im sure you know how to continue this.






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        You should assign letters to the unknown quantities and form simultaneous equations from them.



        I would let the jar's weight be $J$ and the total weight of the cookies be $C$.



        The first statement tells you:



        $$J+C=700tag 1$$



        Then Meghan eats $frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:



        $$J +frac15 C = 400 tag 2$$



        You now have a pair of simultaneous equations. Im sure you know how to continue this.






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          You should assign letters to the unknown quantities and form simultaneous equations from them.



          I would let the jar's weight be $J$ and the total weight of the cookies be $C$.



          The first statement tells you:



          $$J+C=700tag 1$$



          Then Meghan eats $frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:



          $$J +frac15 C = 400 tag 2$$



          You now have a pair of simultaneous equations. Im sure you know how to continue this.






          share|cite|improve this answer









          $endgroup$



          You should assign letters to the unknown quantities and form simultaneous equations from them.



          I would let the jar's weight be $J$ and the total weight of the cookies be $C$.



          The first statement tells you:



          $$J+C=700tag 1$$



          Then Meghan eats $frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:



          $$J +frac15 C = 400 tag 2$$



          You now have a pair of simultaneous equations. Im sure you know how to continue this.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 31 at 22:28









          Rhys HughesRhys Hughes

          7,0501630




          7,0501630























              0












              $begingroup$

              The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let





              • $j$ - weight of jar


              • $n$ - number of cookies at the beginning


              • $c$ - weight of one cookie


              Then you have
              begin{eqnarray}
              j + ncdot c & = & 700 \
              j + frac{n}{5}cdot c & = & 400
              end{eqnarray}
              $$Rightarrow frac{4}{5}cdot ncdot c = 300$$
              $$Rightarrow ncdot c = frac{5}{4}cdot 300 = 375 = 3cdot 5^3$$



              Restricting our consideration to integers you may have at the beginning, for example:





              • $125$ cookies $3g$ each


              • $25$ cookies $15g$ each


              • $15$ cookies $25g$ each

              • etc.






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let





                • $j$ - weight of jar


                • $n$ - number of cookies at the beginning


                • $c$ - weight of one cookie


                Then you have
                begin{eqnarray}
                j + ncdot c & = & 700 \
                j + frac{n}{5}cdot c & = & 400
                end{eqnarray}
                $$Rightarrow frac{4}{5}cdot ncdot c = 300$$
                $$Rightarrow ncdot c = frac{5}{4}cdot 300 = 375 = 3cdot 5^3$$



                Restricting our consideration to integers you may have at the beginning, for example:





                • $125$ cookies $3g$ each


                • $25$ cookies $15g$ each


                • $15$ cookies $25g$ each

                • etc.






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let





                  • $j$ - weight of jar


                  • $n$ - number of cookies at the beginning


                  • $c$ - weight of one cookie


                  Then you have
                  begin{eqnarray}
                  j + ncdot c & = & 700 \
                  j + frac{n}{5}cdot c & = & 400
                  end{eqnarray}
                  $$Rightarrow frac{4}{5}cdot ncdot c = 300$$
                  $$Rightarrow ncdot c = frac{5}{4}cdot 300 = 375 = 3cdot 5^3$$



                  Restricting our consideration to integers you may have at the beginning, for example:





                  • $125$ cookies $3g$ each


                  • $25$ cookies $15g$ each


                  • $15$ cookies $25g$ each

                  • etc.






                  share|cite|improve this answer









                  $endgroup$



                  The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let





                  • $j$ - weight of jar


                  • $n$ - number of cookies at the beginning


                  • $c$ - weight of one cookie


                  Then you have
                  begin{eqnarray}
                  j + ncdot c & = & 700 \
                  j + frac{n}{5}cdot c & = & 400
                  end{eqnarray}
                  $$Rightarrow frac{4}{5}cdot ncdot c = 300$$
                  $$Rightarrow ncdot c = frac{5}{4}cdot 300 = 375 = 3cdot 5^3$$



                  Restricting our consideration to integers you may have at the beginning, for example:





                  • $125$ cookies $3g$ each


                  • $25$ cookies $15g$ each


                  • $15$ cookies $25g$ each

                  • etc.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Sep 29 '18 at 9:39









                  trancelocationtrancelocation

                  13.7k1829




                  13.7k1829






























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