MATH SOLVE

6 months ago

Q:
# 2. A chemist wants to make 4 liters of a 7% acid solution by mixing a 10% acid solution and a 4% acid solution. How many liters of each solution should the chemist use? Write your answer as a complete sentence Be sure to: (a) Define your variable and expressions for the quantities. (b) Write an equation that models the problem. (c) Solve the equation. (d) State the answer in a complete sentence Please help and explain

Accepted Solution

A:

( * = multiplication/multiply/times )

Let x - liters of 10% acid solution needed

4-x = liters of 4% acid solution needed

.1x + .04*(4-x)

-------------------- = .07

4

.1x + .04*(4-x) = 4*.07

.1x + .16 - .04x = .28

.06x = .12

x=2

4-x=2

2 liters of 10% acid solution are needed

2 liters of 4% acid solution are needed

If you're still uncertain, we can check our work as so:

.1x + .04*(4-x)

--------------------- = .07

4

.1 * 2 + .04 * (4-2)

------------------------ = .07

4

.2 + .08

------------ = .07

4

.28 = .07 * 4

.28 = .28

Hope I helped.

Let x - liters of 10% acid solution needed

4-x = liters of 4% acid solution needed

.1x + .04*(4-x)

-------------------- = .07

4

.1x + .04*(4-x) = 4*.07

.1x + .16 - .04x = .28

.06x = .12

x=2

4-x=2

2 liters of 10% acid solution are needed

2 liters of 4% acid solution are needed

If you're still uncertain, we can check our work as so:

.1x + .04*(4-x)

--------------------- = .07

4

.1 * 2 + .04 * (4-2)

------------------------ = .07

4

.2 + .08

------------ = .07

4

.28 = .07 * 4

.28 = .28

Hope I helped.