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The Yardley High School science department can spend no more than $\$3,800$ on textbooks this year. The department needs to buy both Biology textbooks, which cost $\$79$ apiece, and Chemistry textbooks, which cost $\$36$ apiece. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of Biology textbooks $\newline$ $y =$ the number of Chemistry textbooks $\newline$ Choices: $\newline$ (A) $79x + 36y \leq 3,800$ $\newline$ (B) $79x + 36y < 3,800$ $\newline$ (C) $36x + 79y \leq 3,800$ $\newline$ (D) $36x + 79y < 3,800$

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Write a linear inequality: word problems

Full solution

Q. The Yardley High School science department can spend no more than

\$3,800

on textbooks this year. The department needs to buy both Biology textbooks, which cost

\$79

apiece, and Chemistry textbooks, which cost

\$36

apiece.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of Biology textbooks

\newline

y =

the number of Chemistry textbooks

\newline

Choices:

\newline

(A)

79x + 36y \leq 3,800

\newline

(B)

79x + 36y < 3,800

\newline

(C)

36x + 79y \leq 3,800

\newline

(D)

36x + 79y < 3,800

Calculate Biology textbooks cost: Biology textbooks cost $\$79$ each, so the total cost for $x$ Biology textbooks is $79x$ .
Calculate Chemistry textbooks cost: Chemistry textbooks cost $\$36$ each, so the total cost for $y$ Chemistry textbooks is $36y$ .
Set total spending limit: The total spending on textbooks cannot exceed $\$3,800$ , so the sum of the costs for Biology and Chemistry textbooks must be less than or equal to $\$3,800$ .
Formulate inequality: The inequality that represents this situation is $79x + 36y \leq 3,800$ .

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