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Mrs. Fowler took her grandchildren to a baseball game, with plans to spend no more than $\$36$ on snacks. An order of nachos costs $\$4$ and a bag of peanuts costs $\$3$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of nacho orders $\newline$ $y =$ the number of bags of peanuts $\newline$ Choices: $\newline$ (A) $3x + 4y \leq 36$ $\newline$ (B) $4x + 3y < 36$ $\newline$ (C) $4x + 3y \leq 36$ $\newline$ (D) $3x + 4y < 36$

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Write two-variable inequalities: word problems

Full solution

Q. Mrs. Fowler took her grandchildren to a baseball game, with plans to spend no more than

\$36

on snacks. An order of nachos costs

\$4

and a bag of peanuts costs

\$3

.

\newline

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

\newline

x =

the number of nacho orders

\newline

y =

the number of bags of peanuts

\newline

Choices:

\newline

(A)

3x + 4y \leq 36

\newline

(B)

4x + 3y < 36

\newline

(C)

4x + 3y \leq 36

\newline

(D)

3x + 4y < 36

Determine Cost and Inequality: Determine the cost per item and set up the inequality. Mrs. Fowler plans to spend no more than $\$36$ on snacks. An order of nachos costs $\$4$ , which is represented by the variable $x$ , and a bag of peanuts costs $\$3$ , which is represented by the variable $y$ . The inequality will represent the total cost of $x$ orders of nachos and $y$ bags of peanuts being less than or equal to $\$36$ .
Write Inequality: Write the inequality using the given information. The total cost for nachos is $4x$ (since each order of nachos costs $\$4$ ) and the total cost for peanuts is $3y$ (since each bag of peanuts costs $\$3$ ). Since Mrs. Fowler can spend at most $\$36$ , the inequality will be $4x$ (cost of nachos) plus $3y$ (cost of peanuts) is less than or equal to $36$ . This gives us the inequality $4x + 3y \leq 36$ .
Check Against Choices: Check the inequality against the given choices. The inequality we have found is $4x + 3y \leq 36$ , which matches one of the given choices.

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