Question

Herman and Jackie are saving money to pay for college. Herman currently has $15,000 and is working hard to save $1000 per month. Jackie only has $12,000 but is saving $1300 per month. In how many months will they have the same amount of savings? How much will each of them have saved?

Answer 1

Part 1)
`10\ months`

Part 2)
`\$25,000`

Explanation:

Let

y ----> the total amount of savings

x ----> the number of months

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

Herman

The slope is equal to
`m=\$1,000\ per\ month`

The y-intercept is
`b=\$15,000`

substitute

`y=1,000x+15,000` ----> equation A

Jackie

The slope is equal to
`m=\$1,300\ per\ month`

The y-intercept is
`b=\$12,000`

substitute

`y=1,300x+12,000` ----> equation B

Part 1) In how many months will they have the same amount of savings?

equate equation A and equation B

`1,300x+12,000=1,000x+15,000`

solve for x

`1,300x-1,000x=15,000-12,000`

`300x=3,000`

`x=10\ months`

Part 2) How much will each of them have saved?

substitute the value of x=10 months in any of the equations

equation A

`y=1,000(10)+15,000=\$25,000`

equation B

`y=1,300(10)+12,000=\$25,000`