Question

A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?

Choose the equation to match the situation.
A. (0.20)(10) = 0.05x + 0.40x
B. (0.20)(10) = 0.05x + 0.40(10 – x)
C. (0.20)(10) = 0.05(10) + 0.40(10 – x)
D. (0.20)(10) = 0.05(10 – x) + 0.40(10 – x)
Part B

Solution

liters of 5% and
liters of 40%

Answer 1

B.(0.2)(10)=0.05(10)+0.1(10-x)

Answer 2

Question :- A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs ?

Choose the equation to match the situation.

A. (0.20)(10) = 0.05x + 0.40x

B. (0.20)(10) = 0.05(10 - x) + 0.40x

C. (0.20)(10) = 0.05(10) + 0.40(10 – x)

D. (0.20)(10) = 0.05(10 – x) + 0.40(10 – x)

Solution :-

Let us assume that, x litres of 40% solution be mixed with (10 - x) litres of 5% solution , so that scientist can get 10 litres of 20% solution.

So,

→ 40% of x + 5% of (10 - x) = 20% of 10 litres.

→ (40 * x)/100 + {5 * (10 - x)} / 100 = (20 * 10/100)

→ 0.40x + 0.05(10 - x) = 0.20 * 10

Above Equation is Equal to Option (B). Therefore, Equation of option (B) will match the situation.. { value was coming in negative so, i changed the sign. }

Now, Solving the equation we get,

→ 0.40x + 0.05(10 - x) = 0.20 * 10

→ 0.40x + 0.5 - 0.05x = 2

→ 0.40x - 0.05x = 2 - 0.5

→ 0.35x = 1.5

→ x ≈ 4.285 = 4.3 Litres.

Hence,

→ Value of 5% solution = 10 - 4.3 = 5.7 Litres.

∴ 4.3 Litres of 40% solution and 5.7 Litres of 5% solution would be mixed to get 10 Litres of 20% solution .