Question

lucy and james are raising money through pledges for each mile they run. lucy starts the event with $150 already pledged and will receive an additional $10 for each mile she runs. james begins with $120 in pledges and will receive another $15 for every mile he runs. after how many miles will james have raised more money than lucy? let x represent the miles lucy and james will run. write an inequality to represent the situation, then solve the inequality. use the keypad to enter the answers in the boxes. an inequality to represent the situation is \boxed{}. james will have more money raised than lucy after \boxed{} miles.

Explanation:

Step1: Define money raised for each

Lucy: $150 + 10x$, James: $120 + 15x$

Step2: Set up inequality

James > Lucy: $120 + 15x > 150 + 10x$

Step3: Isolate x terms

Subtract $10x$: $120 + 5x > 150$

Step4: Isolate constant terms

Subtract 120: $5x > 30$

Step5: Solve for x

Divide by 5: $x > 6$

Answer:

An inequality to represent the situation is $120 + 15x > 150 + 10x$.
James will have more money raised than Lucy after more than 6 miles.