Question

Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets. Manny would like a mixture of 60% detergent and 40% water in 5-gallon buckets. To make this, he combines some 80/20 mixture with some pure water in each 5-gallon bucket. How many gallons of pure water does Manny add to each 5-gallon bucket? Express your answer as a decimal to the nearest hundredth.

Answer 1

1.25 gallons of pure water

Explanation:

Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets.

0.80 d + 0.20w = 15 gallon

Manny would like a mixture of 60% detergent and 40% water in 5-gallon buckets.

0.60d + 0.40w = 5 gallon

0.80 d + 0.20w = 15 ....... Equation 1

0.60d + 0.40w = 5 ......….. Equation 2

Using elimination method

Multiply Equation 1 with 0.60

Multiply Equation 2 with 0.80

We eliminate d

0.80 d + 0.20w = 15 × 0.6

0.60d + 0.40w = 5 × 0.8

=

0.48d + 1.2w = 9....... Equation 4

0.48d + 3.2w = 4..... Equation 5

Subtract Equation 5 from 4

= - 2.0w = -5

w = -5/-2

w = 2.5 gallons.

Hence: 2.5 gallons/2

= 1.25 gallons.

Therefore, Manny adds 1.25 gallons of pure water.