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Yanyin is loading identical boxes onto a pallet. Each box weighs 35 pounds, and the pallet can hold a maximum of 1,500 pounds. Which of the following inequalities best describes
x, the number of boxes Yanyin can load onto the pallet?
Choose 1 answer:
(A)
x+35 >= 1,500
(B)
x+35 <= 1,500
(C)
35 x >= 1,500
(D)
35 x <= 1,500

Yanyin is loading identical boxes onto a pallet. Each box weighs $35$ pounds, and the pallet can hold a maximum of $1$ , $500$ pounds. Which of the following inequalities best describes $x$ , the number of boxes Yanyin can load onto the pallet? $\newline$ Choose $1$ answer: $\newline$ (A) $x+35 \geq 1,500$ $\newline$ (B) $x+35 \leq 1,500$ $\newline$ (C) $35 x \geq 1,500$ $\newline$ (D) $35 x \leq 1,500$

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Write a linear inequality: word problems

Full solution

Q. Yanyin is loading identical boxes onto a pallet. Each box weighs

35

pounds, and the pallet can hold a maximum of

1

,

500

pounds. Which of the following inequalities best describes

x

, the number of boxes Yanyin can load onto the pallet?

\newline

Choose

1

answer:

\newline

(A)

x+35 \geq 1,500

\newline

(B)

x+35 \leq 1,500

\newline

(C)

35 x \geq 1,500

\newline

(D)

35 x \leq 1,500

Determine Inequality: We need to determine the inequality that represents the maximum weight the pallet can hold in terms of the number of boxes. Each box weighs $35$ pounds, so the total weight of $x$ boxes is $35$ times $x$ , or $35x$ . The pallet can hold a maximum of $1,500$ pounds. Therefore, the total weight of the boxes on the pallet must be less than or equal to $1,500$ pounds. This gives us the inequality $35x \leq 1,500$ .
Check Inequality: To check if the inequality makes sense, we can consider what would happen if $x$ were $1$ . If Yanyin loads one box onto the pallet, the weight would be $35$ pounds, which is less than $1,500$ pounds. This is consistent with the inequality $35x \leq 1,500$ . If $x$ were $43$ , for example, the total weight would be $35 \times 43 = 1,505$ pounds, which exceeds the pallet's capacity. This also agrees with the inequality since $35 \times 43$ is not less than or equal to $1,500$ .

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