Question

1. the function ( y = -4x + 48 ) models the average number of t - shirts sold at a store on october first. the function ( y = 3x + 6 ) models the average number of long sleeve shirts sold after october first, where ( x ) is the number of days after october 1. how many days is the average number of t - shirts sold and the average number of long sleeve shirts the same?

Explanation:

Step1: Set the two functions equal

We want to find when the number of t - shirts sold ($y = - 4x+48$) is equal to the number of long - sleeve shirts sold ($y = 3x + 6$). So we set the two equations equal to each other:
$-4x + 48=3x+6$

Step2: Solve for x

First, add $4x$ to both sides of the equation to get:
$48=3x + 4x+6$
Simplify the right - hand side: $48 = 7x+6$
Then, subtract 6 from both sides:
$48-6=7x$
$42 = 7x$
Divide both sides by 7:
$x=\frac{42}{7}=6$

Answer:

6