GED Math Word Problems: Ratios, Percentages, and Equations

Ratio: keep both parts moving

A paint mix uses 2 cups of blue for every 5 cups of white. A job uses 15 cups of white and the same ratio. How much blue?

Quantities: 2 blue, 5 white, 15 white. The white amount is 15 / 5 = 3 times the recipe. Blue is 2 × 3 = 6 cups.

Check: 6 to 15 is the same ratio as 2 to 5, because both pairs divide by 3. Answering 15 copies the white amount. Answering 7.5 is half of 15 and ignores the given ratio.

Percent: decide what the percent is of

A class fund has $80. They spend 30% of it on snacks and then $14 on notebooks. How much is left?

Thirty percent of 80 is 0.30 × 80 = $24. Then 80 − 24 − 14 = $42.

Check: $24 + $14 + $42 = $80. If you subtract 30% from 14, you answered a different sentence. If you stop at $56, you forgot the notebooks.

Equation: name the unknown before you divide

A community garden charges $12 to join and $3 per visit. Dana has $36 and no other discounts in this example. How many visits use the whole $36?

The unknown is visits, v. The equation is 12 + 3v = 36. Then 3v = 24, so v = 8.

Check: 3 × 8 = 24, and 24 + 12 = 36. Dividing 36 by 3 gives 12 visits, which pretends the join fee is zero.

When the story mixes two of these

A $50 tool is 20% off, then the shop adds a $4 supply fee. Sale price first: 0.20 × 50 = $10, so 50 − 10 = $40. Then 40 + 4 = $44.

The order matters. Adding the fee before the discount would discount the fee too, and the sentence does not say that. Set up one new original problem the same way →: quantities, operation, answer, and a check that uses the original numbers.

The math study guide covers geometry and graphs. The calculator page says when an on-screen calculator is available. Neither page replaces writing the equation first.