A 25% vinegar solution is combined with triple the amount of a 45% vinegar solution and a 5% vinegar solution resulting in 20 milliliters of a 30% vinegar solution.

Question

Mathematics

Quentin Howard

6 March, 08:51

A 25% vinegar solution is combined with triple the amount of a 45% vinegar solution and a 5% vinegar solution resulting in 20 milliliters of a 30% vinegar solution.

+4

Answers (1)

Know the Answer?

Karsyn Brandt · Answer 1

Complete Question: A 25% vinegar solution is combined with triple the amount of a 45% vinegar solution and a 5% vinegar solution resulting in 20 milliliters of a 30% vinegar solution.

Write an equation that models this situation and explain what each part represents in the situation. Then solve the equation.

Step-by-step explanation:

let the volume of the 45% vinegar solution be x litres,

the volume of the 25% vinegar solution be 3x

and the volume of the 5% vinegar solution be y

summation of all gives,

x+3x+y = 20

4x + y = 20

subtracting 4x from both sides to make y the subject of the equation, we have;

y = 20 - 4x

To the concentration:

substituting for the value of x and y into equation x + 3x + y = 20, we have,

.45x +.25 (3x) +.05 (20-4x) =.3 (20)

multiplying through by 100 to make whole figures we have;

45x + 25 (3x) + 5 (20-4x) = 600

45x + 75x + 100 - 20x = 600

120x - 20x + 100 = 600

100x + 100 = 600

subtracting 100 from both sides, we have;

100x = 600 - 100

100x = 500

dividing both sides by 100,

x = 5.