Question

Nelson is fixing up office and must spend less than $7,500 to hire carpenters and painters. Carpenters charge $28 per hour and painters charge $32 per hour

Answer 1

A.
`28x+32y<7500`

B.199 hours

Explanation:

Let carpenters work for x hours and painters work for y hours.

Nelson must spend money <$7500

Carpenters charge per hour=$28

Painters charge per hour=$32

A.We have to write inequalities which represents this situation

According to question

`28x+32y<7500`

B.If hires carpenters work for total time=40 hours

We have to find the maximum number of hours for which painters can work without exceeding the budget.

Substitute the value in above inequality equation then, we get

`28(40)+32y<7500`

`1120+32y<7500`

Subtracting 1120 on both sides

`32y<7500-1120`

`32y<6380`

Divide by 32 on both sides then we get

`y<(6380)/(32)`

`y<199.375`

Hence,painters can work for maximum 199 hours.