Using Ratios

 

Sharing an Amount in a Given Ratio

To divide an amount into a given ratio:

• Add all parts of the ratio to find the total number of parts.
• Divide the total amount by the number of parts to find the value of one part.
• Multiply the value of one part by each part of the ratio to find the individual amounts.
• Check your answer by adding the parts to ensure they total the original amount.

 

Example: Sharing Money in a Ratio

Problem: $\pounds 200$ is to be shared between two people, A and B, in the ratio 5:3.

Step 1: Find Total Number of Parts

$$5 + 3 = 8$$

Step 2: Find the Value of One Part

$$200 \div 8 = 25$$

Step 3: Calculate Each Share

• A receives 5 parts: $$5 \times 25 = 125$$
• B receives 3 parts: $$3 \times 25 = 75$$

Step 4: Check the Answer

$$25 + 75 = 200 \quad \text{Correct}$$

Final Answer: A gets $\pounds 125$, B gets $\pounds 75$.

 

 

 

 

 

Different Types of Ratio Problems

 

1. Ratios Where You Know the Difference Between Two Parts

Example: Sharing Money Based on a Difference

Kerry is given $\pounds 30$ more than Kacey. The money is shared in the ratio 8:5.

Find how much Kerry and Kacey receive.

Step 1: Find the Difference in Parts

$$8 - 5 = 3 \quad \text{(parts difference)}$$

Step 2: Find the Value of One Part

$$30 \div 3 = 10$$

Step 3: Multiply by Ratio Parts

• Kerry receives: $$8 \times 10 = 80$$
• Kacey receives: $$5 \times 10 = 50$$

Final Answer: Kerry gets $\pounds 80$, Kacey gets $\pounds 50$.

 

2. Ratios Where One Quantity is Given

Example: Cabbage Leaves Eaten by Rabbits

Two rabbits, Alfred and Bob, eat cabbage leaves in a ratio of 8:4.

It is known that Alfred eats 12 more cabbage leaves than Bob.

Step 1: Find the Difference in Parts

$$8 - 4 = 4 \quad \text{(parts difference)}$$

Step 2: Find the Value of One Part

$$12 \div 4 = 3$$

Step 3: Find Total Number of Parts

$$8 + 4 = 12$$

Step 4: Find Total Number of Cabbage Leaves

$$12 \times 3 = 36$$

Step 5: Find Individual Amounts

• Alfred eats: $8 \times 3 = 24$
• Bob eats: $4 \times 3 = 12$

Final Answer: Alfred eats 24 cabbage leaves, Bob eats 12 cabbage leaves.

 

3. Combining Two Separate Ratios into One

Sometimes, you are given two ratios and need to combine them into a three-part ratio.

Example: Sharing Money in Two Different Ratios

Kerry and Kacey share money in the ratio 8:5. Kacey also shares money with Kylie in the ratio 1:2.

Find the overall ratio of Kerry:Kacey:Kylie.

Step 1: Match Kacey’s Position in Both Ratios

• First ratio: $K = 5$
• Second ratio: $K = 1$

To make these ratios compatible, scale up the second ratio so Kacey's value matches:

$$1:2 \quad \text{(Multiply by 5)}  \\  5:10$$

Step 2: Combine the Ratios

Since Kacey’s value is now the same, we can merge:

$$8:5:10$$

Final Answer: The ratio of Kerry:Kacey:Kylie is 8:5:10.