C1

 RATIOS & PROPORTIONS

PRACTICE

COMPOUND PROPORTIONS

The equalities of two ratios is called a proportion. A compound proportion is the equality of more than two ratios. 

Direct proportion: is the quantitative relationship between two quantities such that an increase in one quantity causes a proportional increase in the other.

Inverse proportion: is the quantitative relationship between two quantities such that an increase in one quantity causes a proportional decrease in the other.

Rules for Solving Compound Proportions:

1. Identify the magnitudes.

2. Order the magnitudes and their data, placing the unknown at the end.

3. Check if is direct or inverse proportionality. (Identify the proportionality relationship between the magnitude to the unknown datum and the others).

4. Transform the data into proportional fractions. In inverse proportions, operate with inverse fractions.

5. Calculate the value of x.

EXAMPLE: 

EX2:

Si diez grifos tardan 12 horas en llenar un depósito de 15 metros cúbicos. ¿Cuánto tardarán ocho grifos en llenar un depósito de 7 metros cúbicos?

PRACTICE

• A team of workers will build a wall of 400 m² in 15 days if they work 8 hours every day. How long will they take if the wall has 600 m² and they work 10 hours every day. (RTA: 18)

• 195 men working 10 hours a day can finish a job in 20 days. How many men are employed to finish the job in 15 days if they work 13 hours a day? (RTA: 200)

EXAM

• A farmer has needed 294 kilos of food to feed 15 cows for a week. How many kilos of food does the farmer need to feed 10 cows for 30 days? (ASW: 840)

• 6 printers have printed 100 books in 4 days. How many days will it take to print 50 if we have 4 printers? (ASW: 3)

• If 5 trucks transport 120 tons of goods in 2 days: How many goods will 7 trucks transport in 3 days? (ASW: 252)

• In a central post office,  2 machines categorize 1600 packages in 8 hours. How many machines are needed to categorize 2400 packages in 6 hours? (ASW: 4)