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Trevon is going to buy a coat and a hat. The coat costs 3 times as much as the hat. He must spend less than
$94. If the cost of the hat is
x dollars, which inequality best models this situation?
Choose 1 answer:
(A)
3x < 94
(B)
3x > 94
(C)
4x < 94
(D)
4x > 94

Trevon is going to buy a coat and a hat. The coat costs $3$ times as much as the hat. He must spend less than $\$ 94$ . If the cost of the hat is $x$ dollars, which inequality best models this situation? $\newline$ Choose $1$ answer: $\newline$ (A) 3 x<94 $\newline$ (B) 3 x>94 $\newline$ (C) 4 x<94 $\newline$ (D) 4 x>94

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Write two-variable inequalities: word problems

Full solution

Q. Trevon is going to buy a coat and a hat. The coat costs

3

times as much as the hat. He must spend less than

\$ 94

. If the cost of the hat is

x

dollars, which inequality best models this situation?

\newline

Choose

1

answer:

\newline

(A)

3 x<94

\newline

(B)

3 x>94

\newline

(C)

4 x<94

\newline

(D)

4 x>94

Define variables: Let's define the variables. We are given that the cost of the hat is $x$ dollars. Since the coat costs $3$ times as much as the hat, the cost of the coat is $3x$ dollars.
Calculate total cost: To find the total cost of the coat and the hat, we add the cost of the hat and the cost of the coat. The total cost is $x$ (for the hat) plus $3x$ (for the coat), which equals $4x$ dollars.
Set up inequality: We are told that Trevon must spend less than $\$94$ . Therefore, the total cost of the coat and the hat, which is $4x$ dollars, must be less than $\$94$ . This gives us the inequality 4x < 94.
Match with choices: Now we need to match our inequality with the given choices. The correct inequality that models the situation is 4x < 94, which corresponds to choice (C).

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