A chemist has a bottle of 1% acid solution and a bottle of 5% acid solution. She wants to mix the two solutions to get 100 mL of a 4% acid solution. a. Write a

Question

A chemist has a bottle of 1% acid solution and a bottle of 5% acid solution. She wants to mix the two solutions to get 100 mL of a 4% acid solution.

a. Write a system of equations to represent the above situation. Use the variables A to represent the 1% acid solution and B to represent the 5% acid solution.
b. Solve the system of equations to find how much she will use from each bottle to get 100 mL of a 4% acid solution.

Answer 1

You really don't need two equations but if you want two...

 

A+B=100

A=100-B

1%A+5%B=4%*100

0.01A+0.05B=0.04*100

substitute

0.01(100-B)+0.05B=4

1-0.01B+0.05B=4

1+0.04B=4

0.04B=4-1

0.04B=3

4B=300

B=300/4

B=75 ml of the 5% solution

A=100-75=25 ml of the 1% solution

 

using one equation...

1%x+5%(100-x)=4%(100)

0.01x+0.05(100-x)=0.04(100)

0.01x+5-0.05x=4

5-0.04x=4

5-4=0.04x

1=0.04x

100=4x

x=100/4

x=25 ml of the 1% solution and therefore 100-25=75 ml of the 5% solution