Answer: the cost of a cake is $8.5
the cost of a pie is $1.75
Step-by-step explanation:
Let x = the cost of a cake
Let y = the cost of a pie
A boy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. This means that the cost of the 3 cakes and 4 pies is 40-7.5 = $32.5. Therefore,
3x + 4y = 32.5 - - - - - - - -1
If he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75. This means that the cost of the 4 cakes and 3 pies is 40-0.75 = $39.25. Therefore,
4x + 3y = 39.25 - - - - - - - -2
Multiply equation 1 by 4 and equation 2 by 3. It becomes
12x + 16y = 130
12x + 9y = 117.75
Subtracting ,
7y = 12.25
y = 12.25/7 = 1.75
From equation 1,
3x = 32.5 - 4y
3x = 32.5 - 4×1.75 = 32.5 - 7
3x = 25.5
x = 25.5/3 = $8.5
