Answer:
Part 1) [tex]10\ months[/tex]
Part 2) [tex]\$25,000[/tex]
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
[tex]y=mx+b[/tex]
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 [tex]m=\$1,000\ per\ month[/tex]
The y-intercept is [tex]b=\$15,000[/tex]
substitute
[tex]y=1,000x+15,000[/tex] ----> equation A
Jackie
The slope is equal to [tex]m=\$1,300\ per\ month[/tex]
The y-intercept is [tex]b=\$12,000[/tex]
substitute
[tex]y=1,300x+12,000[/tex] ----> equation B
Part 1) In how many months will they have the same amount of savings?
equate equation A and equation B
[tex]1,300x+12,000=1,000x+15,000[/tex]
solve for x
[tex]1,300x-1,000x=15,000-12,000[/tex]
[tex]300x=3,000[/tex]
[tex]x=10\ months[/tex]
Part 2) How much will each of them have saved?
substitute the value of x=10 months in any of the equations
equation A
[tex]y=1,000(10)+15,000=\$25,000[/tex]
equation B
[tex]y=1,300(10)+12,000=\$25,000[/tex]
