Question

y = 40x - 25 and y = 35x - 5 (x = total games and y = amount earned) beth determined that at 135 games, the referee would earn the same salary for each conference game. is she correct? ○ yes, beth is correct. ○ no. she did not find the correct intersection point. ○ no. she only estimated and did not find the exact values. ○ no. she interpreted the solution of (4, 135) incorrectly.

Explanation:

Step1: Set the two equations equal

To find when the earnings are the same, set \(40x - 25 = 35x - 5\).

Step2: Solve for x

Subtract \(35x\) from both sides: \(40x - 35x - 25 = 35x - 35x - 5\) which simplifies to \(5x - 25 = -5\). Then add 25 to both sides: \(5x - 25 + 25 = -5 + 25\) giving \(5x = 20\). Divide both sides by 5: \(x=\frac{20}{5}=4\).

Step3: Analyze Beth's answer

Beth said at \(x = 135\) the earnings are the same, but we found \(x = 4\) is when they are equal. So she did not find the correct intersection point.

Answer:

B. No. She did not find the correct intersection point.