Chapter 7.5, Problem 81STP

To determine

To Find:

If Cho earned $23,500 , how many of each type of deck did she build.

Answer to Problem 81STP

  $\text{Cho builds 4 large desks and 9 small desks}\text{.}$

Explanation of Solution

Given Information:

Cho charges $1500 to build a small deck and $2500 to build a large deck. During the spring and summer, she built 5 more small decks than large decks.

Calculation:

  $\begin{array}{l}\text{Let 's' be the number of small desks that Cho builds}\\ \text{and 'l' be the number of large desks that Cho builds}\text{.}\\ \text{Cost of 1 small desk = \$1500}\\ \Rightarrow \text{Cost of 's' small desks =\$1500}s\\ \text{Cost of 1 large desk = \$2500}\\ \Rightarrow \text{Cost of 'l' large desks =\$2500}l\\ \text{She earned in total =\$23500}\\ \text{So, the system of linear equation representing the given }\\ \text{situation is :}\\ 1500s+2500l=\mathrm{23500...........}(1)\\ \text{Also, she buils 5 more small desks than large desks}\\ \Rightarrow l+5=s\mathrm{..............................}(2)\\ \text{Substitute s = l+5 in equation (1)}\\ \Rightarrow 1500(l+5)+2500l=23500\\ \Rightarrow 1500l+7500+2500l=23500\\ \Rightarrow 4000l+7500=23500\\ \Rightarrow 4000l+7500-7500=23500-\mathrm{7500..............}[\text{Subtract 7500 from each side]}\\ \Rightarrow 4000l=16000\\ \Rightarrow \frac{4000l}{4000}=\frac{16000}{4000}\mathrm{..............................................}[\text{Divide 4000 each side]}\\ \Rightarrow l=4\\ \text{Substitute l=4 in (2)}\\ \Rightarrow s=l+5=4+5=9\\ \text{So, Cho builds 4 large desks and 9 small desks}\text{.}\end{array}$