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Example of word problem solving

Question:

There are 30 gallons of solution containing 5% acid. To make the solution contain 15% acid, how many gallons of acid need to be added?

Solution:

Let x be the gallons of acid need to be added.
In original solution, acid = 30 × 5%
after adding x gallons of acid, total acid = (30 + x) × 15%
relationship: original acid = total acid - added acid
30 × 5% = (30 + x) × 15% - x
remove denominator by multiply 100 in both side of the equation
30 × 5 = (30 + x) × 15 - 100x
remove parentheses
30 × 5 = 30 × 15 + 15x - 100x
move variable terms to the left side of the equation and move constant terms to the right side of the equation.
100x - 15x = 30 × 15 - 30 × 5
combine similar terms
(100 - 15)x = 30(15 - 5)
85x = 300
x = 300/85 = 3.53

Therefore, we need to add 3.53 gallons of acid into the solution to get the new solution which contain 15% acid. Looking for more detail? Please watch the video.