Question

Jill wants to make 15 no of a 40% acid solution by mixing together a 30% acid solution and a 60% acid solution. How much of each solution must she use?

Answer 1

15 no? Don't recognize "no." I'll use "units" instead.

Let f represent the volume of the 40% acid solution.
Let t represent that of the 30% solution, and s that of the 60% solution.

Then s + t = 15 units. Then, (15 units) - s = t

0.30t + 0.60s=(15 units)(0.40)
Mult. this by 100 to elim. fractions: 30t + 60s = 600

Subst (15 units - s) for t, 30 (15-s) + 60s = 600

4500 - 30s + 60s = 600
30s = 150
s = 5 units

Then t = (15 units - 5 units) = 10 units.

Use 10 units of the 30% solution and 5 units of the 60% solution.

Check: Does (10)(.3) + (5)(.6) = (15)(.4)? Yes

Answer 2

x+y=15
0.3x+0.6y=0.4*15=6
solve the system of equation.
Multiply equation one by 0.3: 0.3x+0.3y=4.5
subtract the new from the second equation: 0.3y=1.5
y=5
x=10