How to Solve Probabilities: Word Problems With Proportions

Measurements

• 1

  Read the following word problem: Sally uses 3 cups of flour to make 15 sweet rolls. How many cups of flour would she need to make 45 sweet rolls?

• 2

  Set up a ratio that reflects the information. Use the words first to understand how the mathematical information fits into the formula: Cups of flour / first quantity of rolls = unknown cups of flour / second quantity of rolls.

• 3

  Plug the mathematical information into the appropriate spots in the formula: 3 cups / 15 rolls = x cups / 45 rolls.

• 4

  Cross multiply the denominators by the numerators and set the products equal to each other: 15 * x = 15x and 45 * 3 = 135, so 15x = 135.

• 5

  Divide both sides of the equation by the coefficient of x, which in this case is 15: 15x / 15 = x and 135 / 15 = 9. Simplifying, x = 9 cups of flour.

• 6

  Plug the value of x back into the formula, so 3 / 15 = 9 / 45. Cross multiply the denominators by the numerators. If your math is correct, the products will be the same, i.e., the ratios are equal.

Production Rate

• 7

  Read the following word problem: It takes Sam 20 minutes to burn 10 CDs. How long would it take Sam to burn 13 CDs?"

• 8

  Set up a ratio according to the information. Use words first to stay organized: first number of CDs / number of minutes = second number of CDs / unknown number of minutes.

• 9

  Plug the mathematical information into the formula, so 10 CDs / 20 minutes = 13 CDs / x minutes.

• 10

  Cross multiply the denominators by the numerators and simplify, so 10x = 260.

• 11

  Divide both sides of the equation by 10 and simplify to find that x = 26 minutes.

• 12

  Plug the value of x back into the formula and cross multiply to check for equality: 10 * 26 = 260 and 13 * 20 = 260.

Conversion

• 13

  Read the word problem: Convert six miles to feet. Before setting up a formula, you first need to know how many feet are in one mile (1 mile = 5,280 feet). Now you can write a formula as a ratio based off this information.

• 14

  Write the formula in word form first: first number of miles / number of feet = second number of miles / unknown number of feet.

• 15

  Simplify the ratio to numeric values: 1 / 5,280 = 6 / x.

• 16

  Cross multiply the denominators and the numerators and simplify: x = 31,680 feet.

• 17

  Plug the information back into the formula --- 1 / 5,280 = 6 / 31,680 --- and cross multiply to check your work, finding that 31,680 = 31,680.