Marshall earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a
salary of $51,000, and each year he receives
a $1,500 raise. How many years will it take
before Marshall and Jim earn the same
salary?

Let Marshall's salary be  

S

m

Let Jim's salary be

S

j

Let the count in years be  

n

S

m

=

$

36000

+

4000

n

S

j

=

$

51000

+

1500

n

Set  

S

m

=

S

j

For convenience lets drop the $ symbol

⇒

36000

+

4000

n

=

51000

+

1500

n

Subtract  

1500

n

and

36000

from both sides

4000

n

−

1500

n

=

51000

−

36000

2500

n

=

15000

Divide both sides by 2500

n

=

15000

2500

=

150

25

=

6

Step-by-step explanation:

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240