Question

You are selling T-shirts to raise money for a charity. You sell the T-shirts for $\$10$ each.

Part A
You have already sold 2 T-shirts. How many more T-shirts must you sell to raise at least $\$500$? Explain.
Part B
Your friend is raising money for the same charity and has not sold any T-shirts previously. He sells the T-shirts for $\$8$ each. What are the total numbers of T-shirts he can sell to raise at least $\$500$? Explain.
Part C
Who has to sell more T-shirts in total? How many more? Explain.

Answer 1

Given

Cost of each t-shirt is:$\$10$

Step 1 : Solve for inequality
Solution Part A

As given we have already sold 2 T-shirts.
So by selling these, we earned $=2\times 10=20$
Let the more number of T-shirts must be sell to raise at least$\$500=x$
$\Rightarrow 2+10x\ge 500$

$\Rightarrow 10x\ge 500–2$ [ Subtract $2$ from both sides ]
$\Rightarrow 10x\ge 488$

$\Rightarrow x\ge \frac{488}{10}$ [ Divide by $10$ both sides ]
$\therefore x\ge 48.8$

Hence, we need to sell at least $48$ more t-shirts to raise at least $\$500$.

Step 2 : Solve for inequality
Solution Part B

As given the cost of each T-shirt sold by my friend $=\$8$

Let number of t-shirts he should sell $=y$
The total numbers of T-shirts he can sell to raise at least $\$500$
$\Rightarrow 8y\ge 500$

$\Rightarrow y\ge \frac{500}{8}$ [ Divide by $8$ both sides ]
$\therefore y\ge 62.5$

Hence, my friend need to sell more than $63$ T-shirts to raise at least $\$500$

Step 3 : Find who sells more Tshirt

Solution Part C

As my friend is selling at lower price so my friend has to sell more t-shirt in total.

As calculated in above two parts the more t-shirts sold by my friends is

$\Rightarrow 63-48=15$

Hence, my friend sold $15$ Tshirt more than me.