Question

(Need it by tomorrow!) Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Jeanette has passed 8 scales, whereas her friend Paul has passed 3 of them. Going forward, Jeanette has committed to passing 3 scales per week, and Paul has committed to passing 4 per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?


In _ weeks, the friends will each have passed _ scales.

Answer 1

Let X = the number of weeks.

Jeanette will pass 3 per week, so 3x, and she already passed 8, so Jeanette would be 3x +8

Paul would be 4x + 3

Set them to equal to solve for x ( the number of weeks.)

3x +8 = 4x +3

Subtract 3x from both sides:

8 = x +3

Subtract 3 from both sides:

X = 5

So it will take 5 weeks to be the same.

Replace X with 5 to find the number of scales.

3x + 8 = 3(5) + 8 = 15 +8 = 23

They would have 23 scales.