Ratio Word Problems
Master the bar model method for solving ratio problems
1. Total Given Problems
The Strategy
- Draw a bar model showing the ratio parts
- Calculate the total number of units
- Find the value of 1 unit from the total
- Calculate what's being asked
Example 1: Sharing Money
Anna and Jill share a sum of $50.
The ratio of Anna's money to Jill's money is 2 : 3.
How much money does Jill have?
Solution:
Total units = 2 + 3 = 5 units
5 units = $50
1 unit = $50 ÷ 5 = $10
Jill (3 units) = 3 × $10 = $30
Example 2: Three Children
Ken, Hassan, and Mei share 70 coins.
The ratio of Ken's coins to Hassan's coins to Mei's coins is 3 : 4 : 7.
How many coins does each child have?
Solution:
Total units = 3 + 4 + 7 = 14 units
14 units = 70 → 1 unit = 70 ÷ 14 = 5 coins
Ken (3 units) = 3 × 5 = 15 coins
Hassan (4 units) = 4 × 5 = 20 coins
Mei (7 units) = 7 × 5 = 35 coins
2. Difference Given Problems
The Strategy
- Draw a bar model showing the ratio parts
- Calculate the difference in units (larger − smaller)
- Find the value of 1 unit from the difference
- Calculate what's being asked
Example 3: School Canteen
The ratio of the number of boys to the number of girls in a school canteen is 7 : 4.
There are 12 more boys than girls.
How many girls are there?
Solution:
Difference in units = 7 − 4 = 3 units
3 units = 12
1 unit = 12 ÷ 3 = 4
Girls (4 units) = 4 × 4 = 16 girls
Example 4: Sharing Money (Difference)
Ken and Raju shared a sum of money in the ratio 5 : 3.
Raju received $60 less than Ken.
How much money did Raju receive?
Solution:
Difference = 5 − 3 = 2 units
2 units = $60 → 1 unit = $60 ÷ 2 = $30
Raju (3 units) = 3 × $30 = $90
3. Complex Word Problems
Example 5: Coins Problem
Ken has 21 coins. The number of coins Ken has is of the number of coins Hassan has.
(a) How many coins does Hassan have?
(b) How many coins do they have altogether?
Solution:
Ken's coins are of Hassan's coins. So Hassan has 7 units and Ken has 3 units: Ken : Hassan = 3 : 7
Ken (3 units) = 21 → 1 unit = 21 ÷ 3 = 7 coins
(a) Hassan (7 units) = 7 × 7 = 49 coins
(b) Total = 3 + 7 = 10 units = 10 × 7 = 70 coins
Example 6: Concert Tickets
The ratio of the price of an adult ticket to a child ticket is 5 : 3.
A family of 2 adults and 3 children paid $76 for all tickets.
(a) What was the price of an adult ticket?
(b) How much did 3 child tickets cost?
Solution:
2 adult tickets = 5 × 2 = 10 units
3 child tickets = 3 × 3 = 9 units
Total = 10 + 9 = 19 units
19 units = $76 → 1 unit = $76 ÷ 19 = $4
(a) Adult ticket (5 units) = 5 × $4 = $20
(b) 3 child tickets (9 units) = 9 × $4 = $36
Example 7: Equal Parts Problem
of Lucy's stickers is equal to of Charlene's stickers.
(a) Find the ratio of Lucy's stickers to Charlene's.
(b) Lucy has 28 more stickers than Charlene. How many stickers does Charlene have?
Key insight: of Lucy's stickers = of Charlene's stickers
Draw Charlene's stickers as 5 equal units. Then of Charlene's stickers is 4 units.
So of Lucy's stickers is also 4 units.
All of Lucy's stickers = 3 × 4 = 12 units.
Lucy has 12 units and Charlene has 5 units, all of the same size.
Solution:
(a) Lucy : Charlene = 12 : 5
(b) Difference = 12 − 5 = 7 units
7 units = 28 → 1 unit = 28 ÷ 7 = 4 stickers
Charlene (5 units) = 5 × 4 = 20 stickers
Bar Model Strategy Summary
Total Given
- Add all units
- Total ÷ total number of units = 1 unit
- Multiply to find answer
Difference Given
- Subtract units (larger − smaller)
- Difference ÷ difference in units = 1 unit
- Multiply to find answer
Always draw the bar model first! It helps you see the relationship clearly.