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3 years ago

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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?

1 answer:

Mashutka [201]3 years ago

7 0

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

<em>Herman</em>

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

<em>Jackie</em>

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

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

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