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?

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

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