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Jamil needs $200$ inches of beaded braid for a craft project. The braid is sold in $2$ -yard spools that cost $\$6.50$ each, or by the foot at $\$1.25$ per foot. Find the least amount Jamil can spend to get the braid he needs.

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Linear Inequality Word Problems

Full solution

Q. Jamil needs

200

inches of beaded braid for a craft project. The braid is sold in

2

-yard spools that cost

\$6.50

each, or by the foot at

\$1.25

per foot. Find the least amount Jamil can spend to get the braid he needs.

Convert to Yards: Convert the required length from inches to yards since one yard equals $36$ inches. Jamil needs $200$ inches. $\newline$ Calculation: $200$ inches $\div$ $36$ inches/yard $=$ $5.56$ yards.
Determine Spools Needed: Determine the number of $2$ -yard spools needed. Since each spool contains $2$ yards, we calculate how many spools are required to cover at least $5.56$ yards. $\newline$ Calculation: $5.56$ yards $\div$ $2$ yards/spool = $2.78$ spools. Since Jamil can't buy a fraction of a spool, he needs to purchase $3$ spools.
Calculate Spool Cost: Calculate the cost for $3$ spools. Each spool costs $\$6.50$ . $\newline$ Calculation: $3$ spools $\times$ $\$6.50$ /spool = $\$19.50$ .
Convert to Feet: Alternatively, calculate the cost if Jamil buys the braid by the foot. First, convert the required length from yards to feet (since $1$ yard $= 3$ feet). $\newline$ Calculation: $5.56$ yards $\times 3$ feet/yard $= 16.68$ feet. Rounding up, Jamil needs $17$ feet.
Calculate Foot Cost: Calculate the cost for $17$ feet at $\$1.25$ per foot. $\newline$ Calculation: $17$ feet $\times$ $\$1.25$ /foot = $\$21.25$ .

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