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

1 Answer
Apr 15, 2018

#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.