Patsy

Patsy makes pillows. She needs 232 inches of trim for the edging. Trim costs $5.50 for a 3-yard spool or $1.10 per foot. What is the least amount Patsy can spend to get the trim she needs? Explain your reasoning.

Correct answer:

x =  13.2 USD

Step-by-step explanation:

$$\begin{gathered} 12in=1ft \\ 1yd=3ft \\ a=232\text{in}\to \text{ft}=232:12\text{ft}=19.33333\text{ft} \\ {l}_1=3\text{yd}\to \text{ft}=3\cdot 3\text{ft}=9\text{ft} \\ {n}_1=\lfloor a/l_1\rfloor =\lfloor 19.3333/9\rfloor =2 \\ b=a-n_1\cdot l_1=19.3333-2\cdot 9=\frac{4}{3}\doteq 1.3333\text{ft} \\ {n}_2=\lceil b\rceil =\lceil 1.3333\rceil =2 \\ x=5.5\cdot n_1+n_2\cdot 1.10=5.5\cdot 2+2\cdot 1.10=13.2\text{USD} \end{gathered}$$

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