Question

PLEASE HELP ASAP ALGEBRA 2 QUESTION


3. The manager of a fish store has water that is 10% salt and water that is 25% salt. He needs to fill an aquarium with 10 gallons of water that is 20% salt.
a. Write a system of linear equations that you can use to determine how many gallons of each type of salt water the manager should combine. Be sure to define your variables.
b. Solve the system and determine how many gallons of each type of salt water the manager should combine. Show all your work. Round to 2 decimal places if necessary.

Answer 1

Let x represent the gallons of water that is 10% salt.

Let y represent the gallons of water that is 25% salt.

Now, write the system of equations:

x + y = 10

.10x +.25y = 0.20 • 10


1) To make the system easier to solve, multiply all the terms in .10x +.25y = 0.20(10) by 100 to make them integers.

10x + 25y = 20 • 10

10x + 25y = 200   

2) Solve for x.

x + y = 10

x = 10 - y

3) Substitute x with 10 - y in the other equation.

10(10 - y) + 25y = 200

100 - 10y + 25y = 200

Combine like terms.

100 + 15y = 200

Subtract 100 from both sides.

15y = 100  

y = 20/3 or 6 2/3

4) Now that we have the numerical value of y, solve for the value of x by substituting once more.

a) x + y = 10

x + 20/3 = 10 or x + 6 2/3 = 10 (either equation is fine)

x = 10/3 or x = 3 1/3

The manager should combine 3 1/3 (3.33) gallons of 10% salt water and 6 2/3 (6.67) gallons of 25% salt water.

5) Always check the answers to make sure.

a) x + y = 10

3 1/3 + 6 2/3 = 10

9 3/3 = 10

10 = 10

b) .10x +.25y = 0.20 • 10

.10(3 1/3) +.25(6 2/3) = 0.20 • 10

1/3 + 5/3 = 2

6/3 = 2

2 = 2