Question

PLEASE HELP ASAP ALGEBRA 2 QUESTION

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