Question

. A store sold 14 more colored shirts thanwhite shirts. The white shirts cost $9.95and colors cost $10.50. If a total of $310.60were sold, how many of each type weresold?

Answer 1

Let "w" represent the number of white shirts sold and "c" the number of colored shirts sold.

If they sold 14 more colored shirts than white shirts, then the number of colored shirts sold can be expressed as:

`c=w+14`

Each white shirt cost $9.95 and each colored shirt costs $10.50. In total, they earned $310.60. To determine the total sales, you have to add the earnings for selling "w" white shirts and the earnings from selling "c" colored shirts:

`9.95w+10.50c=310.60`

Using both equations you can determine the number of white and colored shirts sold.

First, replace the first equation in the second one:

`9.95w+10.50(w+14)=310.60`

Now we have established an equation with one unknown, "w", and we can solve it to determine its value:

-Distribute the multiplication on the parentheses term

`\begin{gathered} 9.95w+10.50w+10.50\cdot14=310.60 \\ 9.95w+10.50w+147=310.60 \end{gathered}`

-Add the like terms together

`20.45w+147=310.60`

-Subtract 147 from both sides of the equation

`\begin{gathered} 20.45w+147-147=310.60-147 \\ 20.45w=163.60 \end{gathered}`

-Divide both sides by 20.45

`\begin{gathered} (20.45w)/(20.45)=(163.60)/(20.45) \\ w=8 \end{gathered}`

w=8 This means that 8 white shirts were sold.

Next, using this value you can calculate how many colored shirts were sold

`\begin{gathered} c=w+14 \\ c=8+14 \\ c=22 \end{gathered}`

c=22 indicates that there were 22 colored shirts sold.