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Johnny is building birdhouses in shop class, and he has a total of $349$ nails on hand. A small birdhouse requires $20$ nails and a large birdhouse requires $56$ nails. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of small birdhouses $\newline$ $y =$ the number of large birdhouses $\newline$ Choices: $\newline$ (A) $20 + x + 56 + y < 349$ $\newline$ (B) $20x + 56y < 349$ $\newline$ (C) $20 + x + 56 + y \leq 349$ $\newline$ (D) $20x + 56y \leq 349$

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Write two-variable inequalities: word problems

Full solution

Q. Johnny is building birdhouses in shop class, and he has a total of

349

nails on hand. A small birdhouse requires

20

nails and a large birdhouse requires

56

nails.

\newline

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

\newline

x =

the number of small birdhouses

\newline

y =

the number of large birdhouses

\newline

Choices:

\newline

(A)

20 + x + 56 + y < 349

\newline

(B)

20x + 56y < 349

\newline

(C)

20 + x + 56 + y \leq 349

\newline

(D)

20x + 56y \leq 349

Calculate nails for small birdhouses: Johnny needs $20$ nails for a small birdhouse, so the total nails used for small birdhouses is $20$ times the number of small birdhouses, which is $20x$ .
Calculate nails for large birdhouses: For large birdhouses, Johnny needs $56$ nails each, so the total nails used for large birdhouses is $56$ times the number of large birdhouses, which is $56y$ .
Formulate total nails inequality: Adding the total nails for small and large birdhouses gives us the total nails used, which should be less than or equal to the nails Johnny has, so the inequality is $20x + 56y \leq 349$ .

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