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.
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.