Question

a band rents a studio to record new music. they pay $150 for one day of use of the studio, plus an additional $100 per hour. if they plan to spend at least $250 but no more than $1,100, which graph represents the number of hours that the band can use the studio?

Explanation:

Step1: Set up the inequality

Let \(h\) be the number of hours. The cost function is \(C = 150+100h\).
We know that \(250\leq150 + 100h\leq1100\).

Step2: Solve the left - hand side of the inequality

Subtract 150 from all parts: \(250-150\leq150 + 100h-150\leq1100 - 150\).
\(100\leq100h\leq950\).
Divide all parts by 100: \(\frac{100}{100}\leq\frac{100h}{100}\leq\frac{950}{100}\).
\(1\leq h\leq9.5\).

Answer:

The graph with a closed circle at \(h = 1\) and a closed circle at \(h=9.5\) (the fourth graph in the order of the problem description, assuming the first graph has wrong endpoints, the second graph has wrong lower - bound, the third graph has wrong lower - bound, and the fourth graph has \(h\) starting at \(1\) and ending at \(9.5\)) represents the number of hours.