Three apples and four bananas cost $4.85. Three apples and ten bananas cost $8.75. Find the cost of an apple.

Question

For this problem, identify your variables (define), set up a system of equations (2 equations, 2 variables), and then solve the system. State your answer in terms of the problem. Example:

The sum of two numbers is 92. Their difference is 20. Find the two numbers.

x = first number

y = second number

{x + y = 92

{x - y = 20

Answer 1

Hello, Erica,

The two equations we can use here are: [Let A = number of Apples, and B = number of bananas]

1) 3A + 4B = 4.85

2) 3A + 10B = 8.75

Since we have 3A in both equations, plus I'm lazy, let's subtract 1) from 2):

That gives us

6B = 3.90,

or B = 0.65

Bananas are $0.65 each.

Use this in either equation to find the value of A:

3A + 4B = 4.85

3A + 4*(0.65) = 4.85

3A + 2.60 = 4.58

3A = 2.25

A = 0.75

Apples are $0.75 each.

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Check by using the original equations:

1) 3*(0.75) + 4*(0.65) = 4.85 ? Yes

2) 3*(0.75) + 10*(0.65) = 8.75 ? Yes