an art teacher has 5 gallons of a mixture that is 80 %paint and 20%water . If she needs to thin the paint mixture so that it is 20% paint and 80% water ,how many gallons of water should she add

Answer 1

By alligation:

HAVE..........WANT...........NEED.........

80%..................................20............

....................20.................................

0%....................................60............

So you need 20 parts of the 80% paint and 60 parts of the 0% paint, i.e. water

Since it is stated that 5 gallons is the 80% that means 5 gallons = 20 parts

Thus, 60 parts must be 15 gallons. So, 15 gallons of water must be added

By algebra:

80% of 5 gallons = 0.80 x 5 = 4.0 gallons of pure paint

4 gallons is 20% of what volume (gallons)? 0.20 x = 4 and x = 20 gallons

So, the final volume of paint must be 20 gallons. Since you start with 5 gallons, you must add 15 gallons water.

(80%)(5 gal) + (0%)(x gal) = (20%)(x gal)

400 = 20x

x = 20 gallons

20 gallons - 5 gallons = 15 gallons of water