Question

2 Justin has $110 to spend at the mall. He wants to buy a hat that costs $25 and a pair

of jeans that cost $40. He is also thinking about buying some bags of socks that cost
$12 each. There is no tax on any of his purchases.
Which statements are true?
Choose all that apply.
A
If x is the number of bags of socks Justin can buy, then the inequality
representing this situation is x < 3.
B
If Justin buys the hat and the jeans, solving the inequality 12x + 65 = 110 for x
will tell him the maximum number of bags of socks he can buy.
C
If Justin buys the hat but not the jeans, solving the inequality 12x + 40 = 110
for x will tell him the maximum number of bags of socks he can buy.
D
If Justin buys the hat, jeans, and the maximum number of bags of socks, he will
have enough money left to buy a belt that is on sale for $7.99.

Answer 1

Option B If Justin buys the hat and the jeans, solving the inequality
`12x+65\leq 110` for x, will tell him the maximum number of bags of socks he can buy

Option D. If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99

Explanation:

Let

x ----> the number of bags of socks

we know that

The number of bags of socks that Justin can buy multiplied by it cost, plus the cost of the hat plus the cost of a pair of jeans, must be at most $110

so

The inequality that represent this situation is

`12x+25+40\leq 110`

solve for x

Combine like terms left side

`12x+65\leq 110`

subtract 65 both sides

`12x\leq 45`

Divide by 12 both sides

`x\leq 3.75`

The maximum number of bags of socks is 3

If Justin buys the hat but not the jeans, then the inequality that represent this situation is

`12x+25\leq 110`

Verify each statement

case A) If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3

The statement is false

The inequality that represent this situation is
`x\leq 3.75`

The maximum number of bags of socks is 3

case B) If Justin buys the hat and the jeans, solving the inequality
`12x+65\leq 110` for x, will tell him the maximum number of bags of socks he can buy

The statement is true

see the explanation

case C) If Justin buys the hat but not the jeans, solving the inequality
`12x+40\leq 110` for x will tell him the maximum number of bags of socks he can buy

The statement is false

Because the inequality will be
`12x+25\leq 110`

case D) If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99

The statement is true

Because

The total cost is

`12(3)+25+40=\$101`

The amount of money left is
`\$110-\$101=\$9`

`\$9 > \$7.99`

therefore

If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt