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At a pancake breakfast, children are served $1$ pancake and adults are served $3$ pancakes. Together, they can be served at most $112$ pancakes, the total number made by the chef. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of children $\newline$ $y =$ the number of adults $\newline$ Choices: $\newline$ (A) $3x + y \leq 112$ $\newline$ (B) $3x + y < 112$ $\newline$ (C) $x + 3y < 112$ $\newline$ (D) $x + 3y \leq 112$

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Write a linear inequality: word problems

Full solution

Q. At a pancake breakfast, children are served

1

pancake and adults are served

3

pancakes. Together, they can be served at most

112

pancakes, the total number made by the chef.

\newline

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

\newline

x =

the number of children

\newline

y =

the number of adults

\newline

Choices:

\newline

(A)

3x + y \leq 112

\newline

(B)

3x + y < 112

\newline

(C)

x + 3y < 112

\newline

(D)

x + 3y \leq 112

Children Pancake Calculation: Children get $1$ pancake each, so for $x$ children, they get $x$ pancakes. $\newline$ Calculation: $1$ pancake/child $\times x$ children = $x$ pancakes.
Adults Pancake Calculation: Adults get $3$ pancakes each, so for $y$ adults, they get $3y$ pancakes. $\newline$ Calculation: $3$ pancakes/adult $\times y$ adults = $3y$ pancakes.
Total Pancake Limit Calculation: The total number of pancakes served to both children and adults cannot exceed $112$ . $\newline$ Calculation: $x$ pancakes for children + $3y$ pancakes for adults $\leq 112$ pancakes.
Combine Calculations for Inequality: Combine the calculations for children and adults to form the inequality. $\newline$ Calculation: $x + 3y \leq 112$ .

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