Question

Translate the word problem below into an equation; then solve.

(e) 24. The royal physician failed to produce a cure for the prince's laziness (see practice
problem e), but the queen said she would still let the physician live if he could find a
cure for her husband's snoring instead. Now the physician is nervously combining a 10
ounce substance containing 6% cottonseed with another substance containing 12%
cottonseed to (hopefully) create a snore-suppressing substance with 8% cottonseed.
How many ounces of the 12% substance must he use?

Answer 1

The Answer is actaully 5

Explanation:

Answer 2

The amount of ounces, Y, of the 12% substance is 3.33 ounces

Explanation:

The word problem has the task of discovering the required amount of the substance containing the 12% cottonseed required to create a snore suppressing substance with 8% cottonseed

Let the amount of the substance with 6% cottonseed in the 10 ounce substance be X and the amount of the substance with 12% cottonseed be Y

We have;

X×6% + Y×12% = 10 ounce × 8%

Which gives;

0.06×X + 0.12×Y = 0.08×10..........(1)

X + Y = 10.....................................(2)

Putting X = 10 - Y, we have;

0.06×(10 - Y) + 0.12×Y = 0.08×10

0.6 - 0.06·Y + 0.12·Y = 0.8

0.06·Y = 0.8 - 0.6 = 0.2

Y = 0.2/0.06 = 10/3 = 3.33 ounces

X = 10 - Y = 10 - 3.33 = 6.67 ounces

Therefore, the amount of ounces, Y, of the 12% substance = 3.33 ounces.