Question

use the table to figure out how many feet of each decoration you need to buy.

ribbon costs $3 per foot. how much will it cost to buy the ribbon?

lights cost $4 per foot. how much will it cost to buy the lights?

Explanation:

Step1: Calculate the cost of ribbon

The total length of ribbon is \(12\frac{2}{3}\) feet. The cost per - foot is \(\$3\).
We use the formula \(Cost = Length\times Cost\ per\ unit\).
First, convert \(12\frac{2}{3}\) to an improper fraction: \(12\frac{2}{3}=\frac{12\times3 + 2}{3}=\frac{36+2}{3}=\frac{38}{3}\)
Then, \(Cost=\frac{38}{3}\times3\)
\(\frac{38}{3}\times3 = 38\)

Step2: Calculate the cost of lights

The total length of lights:
Convert \(3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}\) and \(7\frac{3}{4}=\frac{7\times4+3}{4}=\frac{31}{4}\)
\(Total\ length=\frac{7}{2}+\frac{31}{4}\)
Find a common denominator (4): \(\frac{7\times2}{2\times2}+\frac{31}{4}=\frac{14 + 31}{4}=\frac{45}{4}=11\frac{1}{4}\)
The cost per - foot is \(\$4\)
Using the formula \(Cost = Length\times Cost\ per\ unit\)
\(Cost=\frac{45}{4}\times4\)
\(\frac{45}{4}\times4=45\)

Answer:

The cost to buy the ribbon is \(\$38\).
The cost to buy the lights is \(\$45\).