Question

Billy purchased $100$ shirts at a cost of $\$15$ each and planned to resell them. The first week he sold some of them for $\$25$ each. The second week he sold the rest for $\$20$ each. If his total profit was $\$600$, how many shirts did he sell the first week?

Answer 1

Let the number of shirts he sold the first week = x and the number sold the second week = 100 - x

So we have

[Sales] - [Cost] = Profit

[25x + 20(100 - x)] - [15 * 100] = 600 simplify

25x + 2000 - 20x - 1500 = 600

5x + 500 = 600 subtract 500 from both sides

5x = 100 divide both sides by 5

x = 20 = the number of shirts sold the first week

Explanation:

Answer 2

20

Explanation:

Let x = number of shirts sold in Week 1

Let y = number of shirts sold in Week 2

Profit = Selling price - cost price

If Billy purchased the shirts at a cost of $15 each, then

• Week 1: Profit per shirt = $25 - $15 = $10
• Week 2: Profit per shirt = $20 - $15 = $5

Equation 1

Total of 100 shirts purchased:

⇒ x + y = 100

Equation 2

Total profit of $600:

⇒ 10x + 5y = 600

Rewrite Equation 1 to make y the subject:

⇒ y = 100 - x

Substitute this into Equation 2 and solve for x:

⇒ 10x + 5(100 - x) = 600

⇒ 10x + 500 - 5x = 600

⇒ 10x - 5x + 500 = 600

⇒ 5x + 500 = 600

⇒ 5x = 600 - 500

⇒ 5x = 100

⇒ x = 100 ÷ 5

⇒ x = 20

Therefore, Billy sold 20 shirts in his first week.