Chapter 6.5, Problem 37PPS

(a)

To determine

To Find:The equation relating the cost c to the number of yards n for each material.

Answer to Problem 37PPS

  $\begin{array}{cc}\text{Material}& \text{Function}\\ \text{Ribbon}& c=0.89n\\ \text{Fleece}& c=4.75n\\ \text{Quilting Fabric}& c=2.99n\\ \text{Satin Fabric}& c=3.45n\end{array}$

Explanation of Solution

Given:The below table show price of difference materials.

  $\begin{array}{cc}\text{Material}& \text{Price for length}\\ \text{Ribbon}& \$2.67\text{ for 3 yards}\\ \text{Fleece}& \$9.50\text{ for 2 yards}\\ \text{Quilting Fabric}& \$11.96\text{ for 4 yards}\\ \text{Satin Fabric}& \$10.35\text{ for 3 yards}\end{array}$

  $\begin{array}{cc}\text{Material}& \text{Price for length}\\ \text{Ribbon}& \$2.67\text{ for 3 yards}\\ \text{Fleece}& \$9.50\text{ for 2 yards}\\ \text{Quilting Fabric}& \$11.96\text{ for 4 yards}\\ \text{Satin Fabric}& \$10.35\text{ for 3 yards}\end{array}$

For material Ribbon $2.67 for 3 yards.

Rate of Ribbon per yards $\frac{2.67}{3}\approx 0.89$

Therefore, the function is $c=0.89n$

For material Fleece $9.50 for 2 yards.

Rate of Fleece per yards $\frac{9.50}{2}\approx 4.75$

Therefore, the function is $c=4.75n$

For material Quilting Fabric $11.96 for 4 yards.

Rate of Quilting Fabric per yards $\frac{11.96}{4}\approx 2.99$

Therefore, the function is $c=2.99n$

For material Satin Fabric $10.35 for 3 yards.

Rate of Satin Fabric per yards $\frac{10.35}{3}\approx 3.45$

Therefore, the function is $c=3.45n$

(b)

To determine

To describe: The golden ratio of each objects.

Answer to Problem 37PPS

  

The material cost least per yard is ribbon.

The material cost most per yard is Fleece.

Explanation of Solution

Given:The table shown rate of each material.

  $\begin{array}{cc}\text{Material}& \text{Function}\\ \text{Ribbon}& c=0.89n\\ \text{Fleece}& c=4.75n\\ \text{Quilting Fabric}& c=2.99n\\ \text{Satin Fabric}& c=3.45n\end{array}$

Using table to graph each material on same coordinate plane.

  

The material cost least per yard is ribbon.

The material cost most per yard is Fleece.

The rate is maximum shown most cost per yard.

(c)

To determine

To find: The cost to buy 18 inches of ribbon and 10 meters of fleece.

Answer to Problem 37PPS

Ribbon cost = $0.45

Fleece cost = $51.97

Explanation of Solution

Given:The table shown rate of each material.

  $\begin{array}{cc}\text{Material}& \text{Function}\\ \text{Ribbon}& c=0.89n\\ \text{Fleece}& c=4.75n\\ \text{Quilting Fabric}& c=2.99n\\ \text{Satin Fabric}& c=3.45n\end{array}$

The cost function of ribbon is $c=0.89n$

Where, n represents in yards. So, first change 18 inches to yard.

Therefore, $18\text{ in}=0.5\text{ yard}$

Cost of 18 inches ribbon $=0.89\times 0.5=0.45$

Hence, cost of 18 inches ribbon is $0.45

The cost function of fleece is $c=4.75n$

Where, n represents in yards. So, first change 10 meters to yard.

Therefore, $10\text{ m}=10.94\text{ yard}$

Cost of 10 metersfleece $=4.75\times 10.94=51.97$

Hence, cost of 10 metersfleece is $51.97