[Solved] Ivan and Tanya share £150 in a ratio of 4: 1. Work out how much more Ivan gets compared to Tanya

Ivan and Tanya share £150 in a ratio of 4: 1. Work out how much more Ivan gets compared to Tanya.

Step 1: Understand the problem

Ivan and Tanya share £150 in a ratio of 4:1. We need to find out how much more Ivan gets compared to Tanya.

Step 2: Find the total number of parts in the ratio

The ratio of Ivan’s share to Tanya’s share is 4:1. To find the total number of parts in the ratio, we add the values of the two parts:

4 + 1 = 5

This means that the £150 is divided into 5 parts.

Step 3: Find the value of one part

To find the value of one part, we divide the total amount (£150) by the total number of parts (5):

£150 ÷ 5 = £30

So, one part of the ratio is worth £30.

Step 4: Find Ivan’s and Tanya’s shares

We can find out how much Ivan and Tanya each get by multiplying their respective parts by the value of one part:

Ivan’s share = 4 parts × £30/part = £120 Tanya’s share = 1 part × £30/part = £30

Therefore, Ivan gets £120 – £30 = £90 more than Tanya.

Step 5: Check the answer

We can check the answer by verifying that the ratio of Ivan’s share to Tanya’s share is indeed 4:1:

Ivan’s share / Tanya’s share = £120 / £30 = 4

This confirms that Ivan gets four times the amount that Tanya gets, which is what we expect from a ratio of 4:1.

Therefore, Ivan gets £90 more than Tanya.

Concept used

The concept used in this problem is proportion and ratio. The total amount is divided into parts according to the given ratio, and then each part is multiplied by a common factor to find the actual amount for each part.

The difference between the parts is then calculated to find the difference in the amount received by each person.

Step-by-Step Explanation

Step 1

The ratio of Ivan and Tanya’s shares is 4:1, which means Ivan gets 4 parts and Tanya gets 1 part.

Step 2

To find out how much each part is worth, we divide the total amount (£150) by the sum of the ratio (4 + 1 = 5). This gives us £30 per ratio point.

Step 3

To determine how much Ivan gets, we multiply the £30 per ratio point by the number of ratio points in Ivan’s share (4). This gives us £120.

Step 4

To determine how much Tanya gets, we multiply the £30 per ratio point by the number of ratio points in Tanya’s share (1). This gives us £30.

Step 5

To find out how much more Ivan gets compared to Tanya, we subtract Tanya’s share (£30) from Ivan’s share (£120). This gives us £90.

So Ivan gets £90 more than Tanya.

Therefore the answer is £90.

Method 2

Solution: Given that Ivan and Tanya share in a ratio of 4:1.

Let 4x be Ivan’s money and x be Tanya’s money.

According to the question.

4x + x = 50

5x = 150

x = 30

We know that Ivan gets 4x money.

Substituting the value of x, we get

4(30) = £120

⟹Ivan gets four parts, i.e. £120, and Tanya gets 1 part, i.e. £30

Now, the difference between the share of Ivan and Tanya

£120 – £30

£90

Hence, Ivan gets £90 more than Tanya.

Conclusion

Ivan and Tanya share £150 in a ratio of 4: 1. Ivan gets £90 more than Tanya.