Answer:
14 years
Step-by-step explanation:
[tex]y[/tex] represents number of years it will take for Lenny and Karl to earn same salary.
Lenny make $55,000 and annual raise is $2,500 per year.
So, in [tex]y[/tex] years Lenny would make in dollars = [tex]55,000+2,500y[/tex]
Karl makes $62,000 with annual raises of $2,000 per year.
So, in [tex]y[/tex] years Karl would make in dollars = [tex]62,000+2,000y[/tex]
We know that their salaries would be equal.
So, we have
[tex]55000+2500y=62000+2000y[/tex]
subtracting both sides by [tex]2000y[/tex]
[tex]55000+2500y-2000y=62000+2000y-2000y[/tex]
[tex]55000+500y=62000[/tex]
Subtracting both sides by 55000
[tex]55000+500y-55000=62000-55000[/tex]
[tex]500y=7000[/tex]
Dividing both sides by 500.
[tex]\frac{500y}{500}=\frac{7000}{500}[/tex]
[tex]y=14[/tex]
∴ In 14 years Lenny and Karl would make same salary.
