Question

100Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items were sold prior tothe online launch date.The equation below represents the number of belts sold, S., x days after its-online launch.S = 35The equation below represents the number of wallets sold. S. x days after its online launch.S = 4x + 15Using graphing technology, complete the statements.Afterdays, the total number of belts sold will be the same as the total number of wallets sold.The number of belts and the number of wallets Mr. Matthew sold after this many days is

Answer 1

Use a graphing tool to plot the equations:

`\begin{gathered} S=3^x\quad\text{ \lparen blue\rparen} \\ \\ S=4x+15\quad\text{ \lparen red\rparen} \end{gathered}`

The graphs of the given equations are shown:

As we can see, the graphs intersect at the point (3,27), which means that both equations have the same value when x=3, and in both cases, S=27 for that value.

This means that after 3 days, the number of items sold is the same for both cases. After 3 days, the number of items sold in both cases is 27.

Therefore, the answers are:

After 3 days, the total number of belts sold will be the same as the total number of wallets sold.

The number of belts and the number of wallets Mr. Matthew sold after this many days is 27.