Question

Alex and Blake share some money in the ratio 2 : 5. Blake receives £150 more than Alex. How much money does Alex receive?

Answer 1

Alex receives £100. The ratio of their shares is 2:5, and Blake gets £150 more than Alex. By setting up an equation based on the ratio, we find that the value of each part (x) is £50, resulting in Alex's share being 2 times £50.

Step-by-step explanation:

Alex and Blake share money in a ratio of 2:5, which means that for every 2 parts Alex gets, Blake gets 5 parts. Since Blake receives £150 more than Alex, we can use this information to solve for the amount of money Alex receives.

Let the amount Alex receives be 2x and the amount Blake receives be 5x. The difference between what Blake and Alex receive is 3x, which equals the £150 more Blake has.

So, 3x = £150. To find the value of x, we divide both sides of the equation by 3:

x = £150 ÷ 3

x = £50

Now that we have the value of x, we can calculate how much Alex receives by multiplying 2 by £50:

Alex's share = 2x = 2(£50) = £100

Hence, Alex receives £100.

Answer 2

By setting up an equation based on the ratio 2:5 and the fact that Blake receives £150 more than Alex, we solve for 'x' to find that Alex receives £100.

Step-by-step explanation:

The question is asking us to determine the amount of money Alex receives if he and Blake share money in the ratio 2:5 and Blake receives £150 more than Alex. To solve this, we can set up algebraic expressions for the amounts that Alex and Blake receive and use the given information about the difference in their amounts to find the solution.

Firstly, let us assume that the amount of money Alex receives is 2x and the amount that Blake receives is 5x (since the ratio is 2:5), where 'x' is a common multiple. According to the problem, Blake gets £150 more than Alex which gives us the equation:

5x = 2x + £150

Solving for 'x', we can then find out what Alex receives:

1. 5x = 2x + £150
2. Subtract 2x from both sides: 3x = £150
3. Divide both sides by 3: x = £50
4. Alex's amount (2x) is therefore: 2 × £50 = £100

Alex receives £100.