HELP ME solving a value mixer problem using a system of liner equation

Question

The Adams family and the Russell family each used their sprinklers last summer. The water output rate for the Adams family's sprinkler was 35L

 per hour. The water output rate for the Russell family's sprinkler was 30L

 per hour. The families used their sprinklers for a combined total of 60

 hours, resulting in a total water output of 1975L

. How long was each sprinkler used?

Note that the ALEKS graphing calculator can be used to make computations easier.

Answer 1

The system of equations is:

A+R=60

35A+30R=1975

You can use substitution or elimination to solve. Using substitution:

A=60-R

35(60-R)+30R=1975

2100-5R=1975

-5R=-125

R=25 liters

If R=25 then A=60-25=35 liters

Answer 2

Let's first set up equations based on the information known. Let's have A be the number of hours the Adams family ran their sprinkler and R be the number of hours the Russel family used their sprinkler.

From, "The families used their sprinklers for a combined total of 60 hours", we get A + R = 60 (Equation 1)

From, "Adams family's sprinkler was 35L per hour. The water output rate for the Russell family's sprinkler was 30L per hour....resulting in a total water output of 1975L", we get 35A + 30R = 1975. (Equation 2)

Let's use the Substitution method to solve.

From Equation 1, let's subtract R from both sides to isolate A.

A+R=60 (Equation 1)

(subtract R from both sides)

A = 60 - R

Now we can sub the value for A into Equation 2.

35A + 30R = 1975 (Equation 2)

(sub 60-R for A)

35(60-R) + 30R = 1975

(multiple through the 35 into the parentheses)

2100 - 35 R + 30R = 1975

(combine the Rs)

2100 - 5R = 1975

(subtract 2100 form both sides)

-5R = -125

(divide both sides by -5)

R = 25

Now plug this back into either Equation 1 or 2 and solve for A. I will use Equation 1.

A+R=60 (Equation 1)

(sub 25 for R)

A + 25 = 60

(subtract 25 from both sides)

A = 35

Adams family ran sprinkler for 35 hours. Russel family ran for 25 hours. You can confirm this by plugging these value both back into Equation 2 (or Equation 1 if you used Equation 2 in the previous step).