Question

At the beginning of the year, Alyssa had $100 in savings and saved an additional $7

each week thereafter. Colton started the year with $55 and saved $10 every week. Let
A represent the amount of money Alyssa has saved t weeks after the beginning of the year and let C represent the amount of money Colton has saved t weeks after the
beginning of the year. Write an equation for each situation, in terms of t, and determine the famount of money Alyssa and Colton have saved in the week that they have the same amount of money saved.

Answer 1

A = 7t + 100 and C = 10t+55 are the equations for each situation and they both will have an amount of $205 after 15 weeks.

Explanation:

Given that:

Alyssa started savings with $100

Saved amount each week = $7

A = Amount of money Alyssa have

t = number of weeks

A = 7t + 100

Colton started savings with $55

Saved amount each week = $10

C = 10t + 55

For same amount;

A = C

7t+100 = 10t+55

100-55=10t-7t

45=3t

3t=45

Dividing both sides by 3

`(3t)/(3)=(45)/(3)\\t=15`

Putting t=15 in Alyssa's equation

A = 7(15)+100

A = 105+100 = $205

Hence,

A = 7t + 100 and C = 10t+55 are the equations for each situation and they both will have an amount of $205 after 15 weeks.