Question

Taylor and Natasha are both saving money.

• Taylor starts her savings with $10 and plans to save $20 a week.
• Natasha's savings plan can be modeled with the function
y = 50 + 15x, where y is the amount in savings and x is the number of
complete weeks.
After how many weeks will Taylor and Natasha have an equal amount
saved?
A. Week 3 B. Week 5 C. Week 8 D. Week 10

Answer 1

The number of completed weeks when Natasha and Taylor will have an equal amount of saved is 8 weeks

Explanation:

The starting amount of Taylor's savings = $10

The amount Taylor plans to save a week = $20

Therefore, the function that models Natasha's saving plan is y = 10 + 20·x

The function that models Natasha's saving plan is y = 50 + 15·x

Where;

y is the amount in savings

x is the number of completed weeks

When the amount of savings, y, of both Natasha and Taylor are equal, we have;

y for Natasha = y for Taylor

Therefore

10 + 20·x = 50 + 15·x

20·x - 15·x = 50 - 10

5·x = 40

x = 40/5 = 8

The number of completed weeks when Natasha and Taylor will have an equal amount of saved, x = 8 weeks