Question

katie and jess are competing to see who can run the most miles over several days. katie has already logged 8 miles and can run 3 miles each day. jess has already logged 17 miles, but can only run 2 miles each day. how many days will it take katie to have logged at least as many miles as jess?
let ( x ) represent the number of days the girls 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 (square).
it will take katie (square) days to have logged at least as many miles as jess.

Explanation:

Step1: Define total miles for each

Katie's total: $8 + 3x$; Jess's total: $17 + 2x$

Step2: Set up inequality

Katie's miles ≥ Jess's miles:
$$8 + 3x \geq 17 + 2x$$

Step3: Isolate x term

Subtract $2x$ from both sides:
$$8 + 3x - 2x \geq 17 + 2x - 2x$$
$$8 + x \geq 17$$

Step4: Solve for x

Subtract 8 from both sides:
$$x \geq 17 - 8$$
$$x \geq 9$$

Answer:

An inequality to represent the situation is $8 + 3x \geq 17 + 2x$.
It will take Katie 9 days to have logged at least as many miles as Jess.