Chapter 6.1, Problem 9E

i.

To determine

To calculate: The total number of roses each decorator bought.

Answer to Problem 9E

Decorator A bought $125$ roses.

Decorator B bought $240$ roses.

Decorator C bought $240$ roses.

Explanation of Solution

Given:

Decorator A bought $5$ bouquets that contained $25$ roses each.

Decorator B bought $20$ bouquets that contained $12$ roses each.

Decorator C bought $40$ bouquets that contained $6$ roses each.

Calculation:

To calculate the number of roses bought by each decorator, multiply the number of bouquets with the number of roses in each bouquet.

For A, the total number of roses bought = $5\times 25=125$

For B, the total number of roses bought = $20\times 12=240$

For C, the total number of roses bought = $40\times 6=240$

ii.

To determine

To calculate: Price per rose for each decorator.

Answer to Problem 9E

Decorator A paid $\$0.96$ for each rose.

Decorator B paid $\$0.85$ for each rose.

Decorator C paid $\$0.75$ for each rose.

Explanation of Solution

Given:

Decorator A paid $\$120$ for $5$ bouquets that contained $25$ roses each.

Decorator B paid $\$204$ for $20$ bouquets that contained $12$ roses each.

Decorator C paid $\$180$ for $40$ bouquets that contained $6$ roses each.

Calculation:

To calculate the price per rose for each decorator, find the unit rate.

A paid $\$120$ for $125$ roses (Total number of roses bought by A as calculated in subpart i). Hence cost per rose will be:

  $\frac{\$120}{125\text{ roses}}$

To find unit rate, make denominator $1$

  $\begin{array}{l}\frac{\$120÷125}{125\text{ roses}÷\text{125}}[\text{Divide numerator and denominator by125]}\\ \Rightarrow \frac{\$0.96}{1\text{ rose}}\text{ [simplify]}\end{array}$

Therefore, A pays $\$0.96$ per rose.

B paid $\$204$ for $240$ roses (Total number of roses bought by B as calculated in subpart i). Hence cost per rose will be:

  $\frac{\$204}{\text{240 roses}}$

To find unit rate, make denominator $1$

  $\begin{array}{l}\frac{\$204÷240}{\text{240 roses}÷240}\text{ [Divide numerator and denominator by 240]}\\ \Rightarrow \frac{\$0.85}{1\text{ rose}}[\text{simplify]}\end{array}$

Therefore, B pays $\$0.85$ per rose.

C paid $\$180$ for $240$ roses (Total number of roses bought by C as calculated in subpart i). Hence cost per rose will be:

  $\frac{\$180}{\text{240 roses}}$

To find unit rate, make denominator $1$

  $\begin{array}{l}\frac{\$180÷240}{\text{240 roses}÷240}[\text{Divide numerator and denominator by 240]}\\ \Rightarrow \frac{\$0.75}{1\text{ rose}}\text{ [simplify]}\end{array}$

Therefore, C pays $\$0.75$ per rose.

iii.

To determine

Which decorator paid the least per rose?

Answer to Problem 9E

Decorator C paid the least per rose.

Explanation of Solution

Given:

Decorator A paid $\$120$ for $5$ bouquets that contained $25$ roses each.

Decorator B paid $\$204$ for $20$ bouquets that contained $12$ roses each.

Decorator C paid $\$180$ for $40$ bouquets that contained $6$ roses each.

Calculation:

As calculated in subpart ii,

Decorator A paid $\$0.96$ for each rose.

Decorator B paid $\$0.85$ for each rose.

Decorator C paid $\$0.75$ for each rose.

Comparing the prices for each rose, it is observed that decorator C paid the least per rose.