1. The document provides examples of word problems involving ratios and proportions. It includes problems about guides and tourists, currency exchange rates, constructing Christmas lanterns from bamboo, and more. 2. The solutions show setting up ratios equal to each other to solve for the unknown quantity. For example, with guides and tourists the ratio of 1 guide to 3 tourists is set equal to the ratio of 4 guides to N tourists to find that there are 12 tourists. 3. Additional examples include problems about men painting a building, filling a tank with pipes, and dividing quantities in specific ratios. The document demonstrates how to set up and solve various ratio and proportion word problems.

1. SAMPLE PROBLEMS
When Mrs. Cruz went to abroad for an educational tour, she noticed that each guide
goes along with three tourists. If there are 4 guides, how many tourists would they bring
around?
Given: 1 guide for 3 tourists Solution: guide:tourists = guide:tourists 1 : 3 = 4 : N N = 4
X 3 N = 12 Answer: 12 tourists
SAMPLE PROBLEMS 2. The exchange rate of peso to a dollar in 2015 is ₱45.00 to $1.
How much will you get for $6.50?
Solution: Given: ₱ 45.00 to $1 Solution: dollar:peso = dollar:peso 1 : 45 = 6.50 : N N =
45 x 6.50 N = 292.50 Answer: ₱ 292.50
SAMPLE PROBLEMS 3. For every 3 metres of bamboo sticks, 5 frames of Christmas
lanterns can be made. How many metres are needed to make 20 frames?
Solution: Given: 3 metres to 5 frames Solution: metres:frames = metres: frames 3 : 5 =
N : 20 N =(20 X 3) ÷ 5 N = 60 ÷ 5 N = 12 Answer: 12 metres
If an increase in quantity results to a decrease in another, then the two quantities are in
inverse proportion. This holds true if a decrease in one quantity
1. Three men can complete a project in 3 weeks. How many men will be needed if the
project is to be completed in a week?
Solution: Given: 3 men in 3 weeks Solution: more men:less men = more weeks: less
week N : 3 = 3 : 1 N =(3 X 3) ÷ 1 N = 9 ÷ 1 N = 9 Answer: 9 men are needed to
complete the project.
2. Twenty men can paint a building in 15 days. How many days will it take 30 men to
paint the same building?
Solution: Given: 20 men in 15 days Solution: more men:less men = more days: less
days 30 : 20 = 15 : N N =(20 X 15) ÷ 30 N = 300 ÷ 30 N = 10 Answer: 10 days
3. Five pipes can fill a tank in 2 hours. In how many hours can 1 pipe fill the same tank?
Solution: Given: 5 pipes in 2 hours Solution: more pipes:less pipes = more hours: less
hours 5 : 1 = N : 2 N =(2 x 5) ÷ 1 N = 10 ÷ 1 N = 10 Answer: 10 hours
If a given whole is to be divided into several parts given a specified ratio, partitive
proportion is used.
Divide 100 in to parts 2:3:5.
Solution: Given: 100 into parts 2:3:5 Solution: 2 units + 3 units + 5 units = 10 units 1 unit
= 100 ÷ 10 1 unit = 10 Therefore, 10 x 2 units = 20 10 x 3 units = 30 10 x 5 units = 50
Answer: 20, 30 and 50
Ruby, Rose and Ann are business partners. They agreed to divide their profits in the
ratio 1:2:3. How much should each receive if the total profit is ₱6000?
Solution: Given: ₱6000 into parts 1:2:3 Solution: 1 unit + 2 units + 3 units = 6 units 1 unit
= 6000 ÷ 6 1 unit = 1000 Therefore, 1000 x 1 unit = 1000 1000 x 2 units = 2000 1000 x
3 units = 3000 Answer: Ruby(₱1000), Rose(₱2000), Ann (₱3000)
Divide a 72-m rope into 3 with the ratio 1:2:5. What is the measure of each rope?
Solution: Given: 72-m rope in the ratio 1:2:5 Solution: 1 unit + 2 units + 5 units = 8 units
1 unit = 72 ÷ 8 1 unit = 9 Therefore, 9 x 1 unit = 9 9 x 2 units = 18 9 x 5 units = 45
Answer: 9m, 18m, 45m