Question

Hugh has to earn at least $400 to meet his fundraising goal. He has only 100 books that he plans to sell at $8 each. Which inequality shows the number of books, x, Hugh can sell to meet his goal?

20 ≤ x ≤ 400
40 ≤ x ≤ 100
50 ≤ x ≤ 400
50 ≤ x ≤ 100

I believe the answer is D but i just want to double check

Answer 1

the total earning would be 100*8=800$
the least earning that he needs is 400$
so is we devide both sides with 8 we get the d
correct answer is d

Answer 2

50 ≤ x ≤ 100 shows the number of books he can sell.

Explanation:

Let, y represents the amount he can earn by selling the books

Since, he wants to earn at least $ 400,

⇒ 400 ≤ y

Also, he has 100 book in which each costs $ 8,

Thus, maximum amount he can earn = The total cost of his books

= 8 × 100

= $ 800,

So, we can write,

y ≤ 800,

⇒ 400 ≤ y ≤ 800 ------(1)

Now, here, x represents the number of books he can buy in which each costs $ 8,

⇒ y = 8x

From equation (1),

`400 \leq 8x \leq 800`

`(400)/(8)\leq (8x)/(8) \leq (800)/(8)`

`\implies 50\leq x \leq 100`

Which is the required inequality.