Question

vivian charges $37.50 to dye hair, as well as $6 per foil. If justin would like to dye and foil his hair for no more than $70, form an inequality to solve the maximum number of foils justin will be allowed to have in his hair

Answer 1

`37.5+6x\leq70\rightarrow inequality`

therefore, the maximum number of foils Justin can have is 5

Step-by-step explanation

Step 1

set the ineequality

Let x represents the number of foils

and

fee : $ 37.50

rate per foil = $ 6 per foil

total : no more than 70 ( so 70 or smaller)

so

total = fee+ ( cost of foils)

the cost of foils can be calculated using

cot of foils= rate*number of foils

replace

cost of foils= 6x

so, the total cost is

total = fee+ ( cost of foils)

total = 37.5+ 6x

`total=37.5+6x`

but, remember the total must be equal or smaller than 70

henc e

`37.5+6x\leq70\rightarrow inequality`

Step 2

now, let's solve the inequality

`\begin{gathered} 37.5+6x\leq70\rightarrow inequality \\ \text{subtract 37.5 in both sides} \\ 37.5+6x-37.5\leq70-37.5 \\ 6x\leq32.5 \\ \text{divide both sides by 6} \\ (6x)/(6)\leq(32.5)/(6) \\ x\leq5.41 \end{gathered}`

as the unit is per foil, we need to use whole numbers, so the answer is

`\begin{gathered} x\leq5.41 \\ x\leq5 \end{gathered}`

therefore, the maximum number of foils Justin can have is 5

I hope this helps you