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Brianna is knitting baby items to sell at a craft fair. She has a total of $1,280$ yards of yarn to use for the items. A pair of booties uses $196$ yards of yarn and a cap uses $187$ yards 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 pairs of booties Brianna can knit $\newline$ $y =$ the number of caps Brianna can knit $\newline$ Choices: $\newline$ (A) $187x + 196y \leq 1,280$ $\newline$ (B) $196x + 187y \leq 1,280$ $\newline$ (C) $187x + 196y \geq 1,280$ $\newline$ (D) $196x + 187y \geq 1,280$

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Write two-variable inequalities: word problems

Full solution

Q. Brianna is knitting baby items to sell at a craft fair. She has a total of

1,280

yards of yarn to use for the items. A pair of booties uses

196

yards of yarn and a cap uses

187

yards 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 pairs of booties Brianna can knit

\newline

y =

the number of caps Brianna can knit

\newline

Choices:

\newline

(A)

187x + 196y \leq 1,280

\newline

(B)

196x + 187y \leq 1,280

\newline

(C)

187x + 196y \geq 1,280

\newline

(D)

196x + 187y \geq 1,280

Calculate Yarn Usage: Determine the amount of yarn used for each item. We are given that a pair of booties uses $196$ yards of yarn and a cap uses $187$ yards of yarn. The variables $x$ and $y$ represent the number of pairs of booties and caps Brianna can knit, respectively.
Write Inequality: Write an inequality that represents the total amount of yarn used. The total yarn used for booties is $196$ yards per pair times the number of pairs ( $x$ ), and the total yarn used for caps is $187$ yards per cap times the number of caps ( $y$ ). The sum of these two amounts must be less than or equal to the total yarn available, which is $1,280$ yards. So, the inequality is $196x + 187y \leq 1,280$ .
Check Against Choices: Check the inequality against the given choices. The correct inequality that matches our calculation is $(B) 196x + 187y \leq 1,280$ .
Standard Form Check: Ensure that the inequality is in standard form. The standard form for an inequality is $Ax + By \leq C$ , where $A$ , $B$ , and $C$ are constants. Our inequality $196x + 187y \leq 1,280$ is in standard form, with $A=196$ , $B=187$ , and $C=1,280$ .

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