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?

type a response

Explanation:

Step1: Set the two functions equal

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

Step2: Solve for x

First, add \(4x\) to both sides of the equation to get \(48 = 3x+4x + 6\). Combining like terms, we have \(48=7x + 6\). Then, subtract 6 from both sides: \(48 - 6=7x\), which simplifies to \(42 = 7x\). Finally, divide both sides by 7: \(x=\frac{42}{7}=6\).

Answer:

The average number of t - shirts sold and the average number of long - sleeve shirts sold are the same after 6 days.