A boy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. If he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75 change instead. How much did he pay for each cake and each pie?
Mathematics · High School · Mon Jan 18 2021
Answered on
Given :
Let the cost of cake be x
And, cost of pie be y
Then, according to question
3x + 4y = 40 - 7.50
3x + 4y = 32.50 …1
4x + 3y = 40 - 0.75
4x + 3y = 39.25 …2
Using elimination method:
Multiplying equation 2 by 4 and equation 1 by 3, we get
9x + 12y = 97.5 …3
16x + 12y = 157 …4
Subtracting equation 4 by 3, we get
16x + 12y - 9x - 12y = 157 - 97.7
7x = 59.5
x = 59.5/7
x = 8.5
Putting value of x in equation 1, we get
3(8.5) + 4y = 32.50
25.50 + 4y = 32.50
4y = 32.50 - 25.50
4y = 7
y = 7/4
y = 1.75
Hence, he paid $8.5 for a cake and $1.75 for a pie.