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

To find when the average number of t - shirts sold and long - sleeve shirts sold are the same, we set \(y=-4x + 48\) equal to \(y = 3x+6\). So we have the equation \(-4x + 48=3x + 6\).

Step2: Solve for x

First, add \(4x\) to both sides of the equation:
\(-4x+4x + 48=3x+4x + 6\)
\(48 = 7x+6\)
Then, subtract 6 from both sides:
\(48 - 6=7x+6 - 6\)
\(42=7x\)
Next, divide both sides by 7:
\(x=\frac{42}{7}=6\)

Answer:

6