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

Answer:

Part 1) $10\ months$

Part 2) $\ 25,000$

Step-by-step 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

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