Question

The cooling system of Ennio’s car contains 7.5 L of coolant, which is `33 1/3%` antifreeze. How much of this solution must be drained from the system and replaced with 100% antifreeze so that the solution in the cooling system will contain 50% antifreeze?

finding the equation and using substitution
the answer is 1.875 litres

Answer 1

`1.875` liters of solution must be drained from the system and replaced with `100%` antifreeze

Explanation:

As the cooling system of Ennio’s car contains `7.5` Liters of coolant and should contain `50%` antifreeze coolant, it must have

`7.5xx50/100=7.5xx1/2=3.75` liter antifreeze.

Let the solution drained be `x` liter. This means

we are left with `(7.5-x)` liters of `33 1/3%` antifreeze i.e.

it has `(7.5-x)xx33 1/3%=(7.5-x)100/3xx1/100`

= `1/3(7.5-x)=2.5-1/3x` liters

As we substitute it with `x` liters of `100%` antifreeze

it becomes `x+2.5-1/3x`

This must be `3.75`

Hence `x+2.5-1/3x=3.75`

or `x-1/3x=3.75-2.5=1.25`

or `2/3x=1.25`

Hence `x=1.25xx3/2=3.75/2=1.875` liters

i.e. `1.875` liters of solution must be drained from the system and replaced with `100%` antifreeze.