Question

type 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 to the online launch date. the equation below represents the number of belts sold, s, x days after its online launch. $s = 3^x$ the equation below represents the number of wallets sold, s, x days after its online launch. $s = 4x + 15$ using graphing technology, complete the statements. after \\(\square\\) 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 \\(\square\\).

Explanation:

Step1: Set equations equal

We need to find $x$ when the number of belts sold equals the number of wallets sold, so set $3^x = 4x + 15$.

Step2: Test integer values for $x$

Test $x=3$: $3^3=27$, $4(3)+15=12+15=27$. Both values are equal.

Step3: Verify the total sold

Substitute $x=3$ into either equation to find the total number of items sold.
$S=3^3=27$ or $S=4(3)+15=27$

Answer:

After $\boldsymbol{3}$ 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 $\boldsymbol{27}$.