Question

A rental company charges $15 plus $4 per hour to rent a bicycle. If Margie does not want to spend more than $27 for her rental, write and solve an inequality to find how many hours she can rent the bicycle and not spend more than $27. Interpret the solution. Show your Work.

Answer 1

3 hours

Explanation:

to understand this

you need to know about:

• inequality
• inequality word problems
• solving word problems

let's create the inequality:

let's every hour be x

first condition

A rental company charges $15

therefore,

15

plus $4 per hour to rent a bicycle.

therefore

15+4x (as per our is x)

last condition

Margie does not want to spend more than $27 for her rental,

therefore,

15+4x≤27 (≤ is because as it says"does not want to spend more than $27"

let's solve:

few things about solving inequality

the direction of the inequality won't change

if

• Add (or subtract) a number from both sides
• Multiply (or divide) both sides by a positive number
• Simplify a side

the direction of inequality will change

if

• Multiply (or divide) both sides by a negative number
• Swapping left and right hand sides

`15 + 4x \leqslant 27`

`step - 2 \colon \: \\ subtract \:15 \: from \: both \: sides`

`15 - 15 + 4x \leqslant 27 - 15`

`4x \leqslant 12`

`step - 3 \colon \: \\ divide \: both \: sides \: by \: 4`

`(4x)/(4) \leqslant (12)/(4)`

`x \leqslant 3`

`\therefore \: she \: can \: rent \: the \: bicycle \: for \: 3 \: hours`

Answer 2

The total cost for X hours is the fixed cost of $15 plus the variable cost of $4 per hour which is equal to 4*X, so the total cost is 4*X + 15

If Margie does not want to spend more than $27 then the inequality is

4*X + 15 <= 27

4*X <= 12

X <= 3

If Margie does not want to spend more than $27 then she cannot rent the bicycle for more than 3 hours