they want both amounts for each solution

Question

A large solar heating panel requires 240 gallons of a fluid that is 55% antifreeze. The fluid comes in either a 65% solution or a 25% solution. How many gallons of each should be used to prepare the 240-gallon solution?

Answer 1

Kaitlyn,

 

Imagine you're using x gallons 65% and y gallons 25% solution. Based on the total amount of liquid we know

x+y=240

 

And based on the amount of antifreeze:

.65x+.25y=240*.55=132

 

To eliminate one of the variables, let's multiply the first equation by -.65 and add it to the second:

-.65x-.65y=-156

.65+.25y=132

-.4y=--24

y=60 gallons 25% solution, which means we need 240-60=180 gallons 65% solution. Let's check our work. 60+180=240 gallons. 180*.65+25*.60=117+15=132 gallons antifreeze=.55*240 Check!

 

Hope that helps!