Ratios, Percentages & Word Problems

Ratios: If the ratio of men to women is 3:5, and there are 40 people total, then 3+5=8 parts, each part = 5, men = 15, women = 25.

Percent change: (New - Old) / Old x 100

$200 to $250 = 25% increase

$250 to $200 = 20% decrease (NOT 25%!)

Successive percents: Multiply the multipliers.

30% increase then 20% decrease: 1.30 x 0.80 = 1.04 = 4% net increase

Work rate problems:

If A does a job in 6 hours and B in 3 hours:

Rate A = 1/6, Rate B = 1/3

Combined rate = 1/6 + 1/3 = 1/2

Together they finish in 2 hours.

Mixture problems: Use the weighted average approach.

Mix 10 liters of 20% solution with 5 liters of 50% solution:

(10 x 0.20 + 5 x 0.50) / 15 = 4.5/15 = 30%

Reference:

Wikipedia: Ratio

https://en.wikipedia.org/wiki/Ratio