Question

Two shoppers buy the following at a fruit,paying the amounts given.

Shopper 1: 4 apples and 3 bananas for $2.59
Shopper 2: 6 apples and 5 bananas for $4.11

a) Decide on pronumeral names for the unknown quantities.
b).write equations involving these pronunerals.work in terms of dollars.
c). Solve for the unknowns.

Answer 1

a) x is the cost of an apple and y is the cost of a banana.

b)

`4x + 3y = 2.59`

`6x + 5y = 4.11`

c) An apple costs $0.31 and a banana costs $0.45.

Explanation:

We have to find the cost, in dollars, of an apple and of a banana.

We do this solving a system of equations.

a) Decide on pronumeral names for the unknown quantities.

I am going to say that:

x is the cost of an apple.

y is the cost of a banana.

b).write equations involving these pronunerals.work in terms of dollars.

4 apples and 3 bananas for $2.59

This means that
`4x + 3y = 2.59`

6 apples and 5 bananas for $4.11

This means that
`6x + 5y = 4.11`

c). Solve for the unknowns.

I am going to use the addition method, multiplying the first equation by 5 and the second by -3, and then adding them. So

20x + 15y = 12.95

-18x - 15y = -12.33

20x - 18x + 15y - 15y = 12.95 - 12.33

2x = 0.62

x = 0.62/2

x = 0.31

And

4x + 3y = 2.59

3y = 2.59 - 4x

3y = 2.59 - 4*0.31

3y = 1.35

y = 1.35/3

y = 0.45

An apple costs $0.31 and a banana costs $0.45.