Carol would like to pay cash for a car when she graduates from college and estimates that she can afford a car that cost between $4000 and $8000. She has saved $500 so far and plans to earn the rest of the money by working the next two summers. If Carol plans to save the same amount each summer, use a compound inequality to find the range of money she must save each summer to buy the car.

Question

Carol would like to pay cash for a car when she graduates from college and estimates that she can afford a car that cost between $4000 and $8000. She has saved $500 so far and plans to earn the rest of the money by working the next two summers. If Carol plans to save the same amount each summer, use a compound inequality to find the range of money she must save each summer to buy the car.

Answer 1

let x = the amount she must save each summer.

She will have twice that amount, plus the 500 she already has. Altogether, that must come to at least 4000, but does not need to exceed 8000.

4000 <= 2x + 500 <= 8000

Solve for x

Answer 2

Let's break down the problem step-by-step:

1. Carol wants to buy a car that costs between $4000 and $8000.
2. She has saved $500 so far.
3. Carol plans to earn the rest of the money by working the next two summers.
4. Carol plans to save the same amount each summer.

To find the range of money Carol must save each summer, we'll use a compound inequality.

Let's denote the amount Carol needs to save each summer as "x".

The amount she needs to save in two summers is then 2x.

To find the range, we use the given condition:
4000 ≤ (500 + 2x) ≤ 8000

Now, we will solve the inequality step-by-step:

1. Subtract 500 from all parts of the inequality:
4000 - 500 ≤ 2x ≤ 8000 - 500

2. Simplify:
3500 ≤ 2x ≤ 7500

3. Divide all parts of the inequality by 2 (since Carol will save the same amount each summer):
3500/2 ≤ 2x/2 ≤ 7500/2

4. Simplify:
1750 ≤ x ≤ 3750

Therefore, the range of money Carol must save each summer to buy the car is between $1750 and $3750.

Answer 3

To find the range of money Carol must save each summer, we need to divide the total amount she needs to save by the number of summers she plans to work.

Carol needs to save the amount between $4000 and $8000. If we subtract the amount she has already saved ($500), we get the remaining amount she needs to save, which is between $3500 and $7500.

Since Carol plans to work for two summers, we will divide the remaining amount by 2:

$3500/2 = $1750
$7500/2 = $3750

Therefore, the range of money Carol must save each summer to buy the car is between $1750 and $3750.

Using a compound inequality, this can be written as:

$1750 ≤ Amount Carol saves each summer ≤ $3750