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Jean spent 3/7 of her money on 2 cupcakes and 8 sardine pies, and 3/4 of the remaining money on 3 pandan cakes. Each cupcake cost twice as much as a sardine pie. Each pandan cake cost $4.50 more than a cupcake. How much did she spend altogether?

 Aug 25, 2021
 #1
avatar+570 
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You don't have to ask for one person specifically. Other people can help too, unless this is a problem you specifically want him/her to answer because of something.

 Aug 25, 2021
 #2
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U answered my question for nothing >:

Guest Aug 25, 2021
 #3
avatar+47 
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Hey Guest! 

Thank you for asking me specifically but as sparkling water said, you don't need to ask for a certain person. 

I'm not quite sure how to approach this problem but this is my best attempt: so each cupcake costs twice as much as a sardine pie, therefore c=2s (c represents cupcake and s represents sardine pie) so the cost of 2 cupcakes and 8 sardine pies is the same as the cost of 12 sardine pies. She then spent 3/4 of her remaining money which is 3/4 of the 4/7 left. This amount is the same as 1/7 of the original amount. The question says that pandan cakes cost 4.50 more than cupcakes but gives no clue as to the other prices. This leaves me at a dead end. You could instead change to amount of sardine pies into cupcakes so the cost of 2 cupcakes and 8 sardine pies is the same as the cost of 6 cupcakes but this still doesn't help us. 

Could someone else try this question? I am new to this website and I do not have a great knowledge of maths so someone else here might be able to help.

 

SCZ

 Aug 25, 2021
 #5
avatar+86 
+1

To determine the amount Jean spent all together, we have to determine the cost of each of cupcakes sardine pies and pandan cakes. For this let S be the total money Jean have with her and let x be  the price of a sardine pies and . 

 

 

 


It is given that each cupcake cost twice as much as a sardine pie. Therefore cost of a cup cake will be 

2x. And it is also given that each pandan cake cost $4.50 more than a cupcake. Therefore the cost of a pandan cake will be 4.5+2x.

 

Now Jean spends 3/7th her money buying 2 cupcakes and 8 sardine pies. which can be represented as an equation as follows;

   3S/7 = 2(2x) + 8x

           = 4x + 8x

           = 12x

∴ 3S/7 = 12x ⋯⋯⋯⋯⋯ (1)

 

 

Now the remaining amount left with her will be;

S - 3S/7 = 7S - 3S/7

              = 4S/7

Now spends 3/4th of this remaining money on 3 pandan cakes which can be represented as an equation as follows;

3/4 ⋅ 4S/7 = 3(2x + 4.5) 

        3S/7 = 6x + 13.5 ⋯⋯⋯⋯⋯ (2) 

Now right hand side of both equation (1) and (2) are the same. So equating the right hand side of the two equations and solving for x as follows;

      12x=6x + 13.5

12x - 6x=13.5

         6x=13.5

           x=13⋅5/6

             =2.25

Therefore the cost of a sardine pies is $2.25 
Therefore the cost of a cup cake is equal to;

2x=2⋅2.25

    =$4.5

And the cost of Pandan pie is equal to;
2x + 4.5=4.5 + 4.5

             =$9


 

 

 

 

Therefore the total amount spend in buying 2 cupcakes 8 sardine pies, and 3 Pandan cake is given by;

total amount = 2(2x) + 8x + 3(2x + 4.5)

                     = 2 ⋅ 4.5 + 8 ⋅ 2.25 + 3 ⋅ 9

                     = 54

Therefore the total amount she have spend is $54. 

 


 

 Aug 26, 2021

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