Question

Suppose a car dealer receives a profit of $500 for each mid-sized car m sold and $750 for each sport-utility vehicle s sold. The dealer must sell at least two mid-sized cars for each sport-utility vehicle and must earn at least $3500 per week. 13Suppose a car dealer sells 2 sport-utility vehicles. How many mid-sized cars must be sold to earn at least $3500?

Answer 1

Take the cost of the sport-utility vehicle and multiply by 2.
750 x 2 =1,500
Take the amount of money the dealer must earn and subtract 1,500.
3,500 - 1,500 = 2,000
Take 2,000 and divide by the cost of a mid-sized car.
2,000 ÷ 500 = 4
The answer is the dealer must sell 4 mid sized cars to make 3,500.

Answer 2

`\boxed{\text{Four}}`

Explanation:

500m = profit on mid-sized cars

750s = profit on SUVs

500m + 750s = total profit

You have two conditions:

(1) 500m + 750s ≥ 3500

(2) m ≥ 2s

Let s = 2

Check condition (1)

500m + 750 × 2 ≥ 3500

500m + 1500 ≥ 3500

500m ≥ 2000

m ≥ 4

Check condition (2)

(2) m ≥ 2 × 2

m ≥ 4

`\text{The dealer must sell }\boxed{\textbf{four}}\text{ mid-sized vehicles per month}}`

Check:

500 × 4 + 750 × 2 ≥ 3500 4 ≥ 2 × 2

2000 + 1500 ≥ 3500 4 ≥ 4

3500 ≥ 3500

OK.