Question

You are at a fruit stand to get some fresh produce. You notice that the person in front of you gets 5

apples and 4 pears for 10 dollars. You get 5 apples and 5 pears for 11 dollars. Write a system of
equations that could be used to find the price of an apple and the price of a pear.

Answer 1

`5A + 4P = 10`

`5A + 5P = 11`

1 apple costs $1.2

1 pear costs $1

Explanation:

Represent Apples with A and Pears with P

For the person in my front, the expression is:

`5A + 4P = 10`

For me, the expression is

`5A + 5P = 11`

Hence, the system of equation is:

`5A + 4P = 10`

`5A + 5P = 11`

Solving for the values of A and P.

Substract equation (2) from (1)

`5A - 5A + 4P - 5P = 10 - 11`

`-P = -1`

`P = 1`

Hence, 1 pear costs $1

Substitute 1 for P in
`5A + 4P = 10`

`5A + 4 * 1 = 10`

`5A + 4 = 10`

`5A = 10 - 4`

`5A = 6`

`A = (6)/(5)`

`A = \$1.2`

Hence, 1 apple costs $1.2