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.
