Solve proportions: word problems

Key notes :-

1. Understanding Proportions

  • A proportion is an equation that states two ratios are equal.
  • It is often written in the form:

where a, b, c, and d are numbers, and b≠0, d≠0.

2. Solving Proportions

  • To solve a proportion, cross-multiply: a×d=b×c
  • After cross-multiplying, solve for the unknown variable.

3. Steps to Solve Word Problems Involving Proportions

  • Step 1: Read the problem carefully and identify the two ratios or fractions.
  • Step 2: Set up the proportion. Write down the ratio using the known values and the unknown variable.
  • Step 3: Use cross-multiplication to find the missing value.
  • Step 4: Solve the equation to find the unknown value.
  • Step 5: Check if the solution makes sense in the context of the problem.

Learn with an example

🔔 Jonah prepared 4 kilograms of dough after working 2 hours. How much dough did Jonah prepare if he worked for 7 hours? Assume the relationship is directly proportional.

______ kilograms

Set up a proportion and solve for n.

4 kilograms / 2 hours = n kilograms / 7 hours

4/2 ( 2 . 7 ) = n/7 ( 2 . 7 ) Multiply both sides by 2 · 7

4 · 7 = 2n Simplify

28 = 2n Multiply

14 = n Divide both sides by 2

If Jonah worked for 7 hours, he prepared 14 kilograms of dough.

🔔 Ronald spent 8 minutes on the phone while routeing 4 phone calls. In all, how many phone calls does Ronald have to route to spend a total of 14 minutes on the phone? Assume the relationship is directly proportional.

______ phone calls

Set up a proportion and solve for n.

8 minutes / 4 phone calls = 14 minutes / n phone calls

8/4 ( 4n ) = 14/n ( 4n ) Multiply both sides by 4n

8n = 14 · 4 Simplify

8n = 56 Multiply

n = 7 Divide both sides by 8

To spend a total of 14 minutes on the phone, Ronald has to route 7 phone calls.

🔔 Rodrigo prepared 4 kilograms of dough after working 2 hours. How much dough did Rodrigo prepare if he worked for 8 hours? Assume the relationship is directly proportional.

____ kilograms

Set up a proportion and solve for n.

4 kilograms / 2 hours = n kilograms / 8hours

4/2 (2 . 8) = n/8 (2 . 8) Multiply both sides by 2 · 8

4 · 8 = 2n Simplify

32 = 2n Multiply

16 = n Divide both sides by 2

If Rodrigo worked for 8 hours, he prepared 16 kilograms of dough.

Let’s Practice!