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? Write and solve an equation to match the solution.
Equation:________________________
Solution:____ liters of 5% and _____ liters of 40%

Answer 1

Answer:

4.286Liters of 40% and 5.71 Liters of 5%.

Step-by-step explanation:

Quantity of 20% acid=10lit.

Therefore amount of concentrated acid needed=(20/100)×10=2liters.

Let the quantity of 5% acid solution be X Liter.

Let the quantity of 40% acid solution be YLiter.

Now as per question X+Y=10........................(1)

Also,( 5/100)×X+(40/100)×Y=2

5X+40Y=200.....................................................(2)

Now we have to solve equation (1)and (2) to get the solution.

Multiplying equation (1) with 5 we get,

5X+5Y=50.............................(3)

Substracting the equation (3) from equation(2) we get,

5X+40Y-5X-5Y=200-50

35Y=150

Y=150/35=4.286Liter.

Therefore, X=10-4.286 =5.71 Liter