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Carly is knitting baby items to sell at a craft fair. She has a total of $1,700$ yards of yarn to use for the items. A pair of booties uses $205$ yards of yarn and a cap uses $191$ 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 Carly can knit $\newline$ $y =$ the number of caps Carly can knit $\newline$ $\newline$ Choices: $\newline$ (A) $205 + x + 191 + y \leq 1,700$ $\newline$ (B) $191x + 205y \leq 1,700$ $\newline$ (C) $205x + 191y \leq 1,700$ $\newline$ (D) $191 + x + 205 + y \leq 1,700$

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Write a linear inequality: word problems

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

1,700

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

205

yards of yarn and a cap uses

191

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 Carly can knit

\newline

y =

the number of caps Carly can knit

\newline

\newline

Choices:

\newline

(A)

205 + x + 191 + y \leq 1,700

\newline

(B)

191x + 205y \leq 1,700

\newline

(C)

205x + 191y \leq 1,700

\newline

(D)

191 + x + 205 + y \leq 1,700

Total Yarn Available: Carly has a total of $1,700$ yards of yarn to use for knitting baby items. We need to find the inequality that represents the maximum number of pairs of booties ( $x$ ) and caps ( $y$ ) she can knit without exceeding the total yarn available.
Yarn Usage Calculation: A pair of booties uses $205$ yards of yarn, so if Carly knits $x$ pairs of booties, she will use $205x$ yards of yarn.
Inequality Representation: A cap uses $191$ yards of yarn, so if Carly knits $y$ caps, she will use $191y$ yards of yarn.
Inequality Representation: A cap uses $191$ yards of yarn, so if Carly knits $y$ caps, she will use $191y$ yards of yarn.To find the total amount of yarn used for $x$ pairs of booties and $y$ caps, we add the yarn used for the booties and the yarn used for the caps: $205x + 191y$ .
Inequality Representation: A cap uses $191$ yards of yarn, so if Carly knits $y$ caps, she will use $191y$ yards of yarn.To find the total amount of yarn used for $x$ pairs of booties and $y$ caps, we add the yarn used for the booties and the yarn used for the caps: $205x + 191y$ .Since Carly cannot use more than $1,700$ yards of yarn, the total amount of yarn used for both booties and caps must be less than or equal to $1,700$ yards. This gives us the inequality $205x + 191y \leq 1,700$ .

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