Share £3.40 among Angela, Ben and Claire. For every 10p Angela gets, Ben gets 5p, and Claire gets 2p.
So -- what is your question?
Angela gets....., Ben gets.....and Claire gets...
sorry
3.4 / .17 = ?
To solve this problem, we need to calculate the amounts that Angela, Ben, and Claire will receive based on the given ratios.
Let's assign variables to their shares:
- Let the amount Angela gets be A
- Let the amount Ben gets be B
- Let the amount Claire gets be C
Given that for every 10p Angela gets, Ben gets 5p and Claire gets 2p, we can write the following equations:
1) A/10 = B/5
2) A/10 = C/2
Now, let's solve these equations step by step.
From equation (1), we can re-write it as:
A = 2B/1
Substituting this into equation (2), we get:
2B/10 = C/2
Simplifying further, we have:
B/5 = C/2
To make the equation easier to work with, let's assume that Ben's share is x.
B = x
Now, we can find C in terms of x:
C = 2B/5 = 2x/5
Furthermore, substitute B and C into equation (2):
A/10 = (2x/5)/2
A/10 = x/5
Now, we can find A in terms of x:
A = 10(x/5) = 2x
Now, we have the amounts Angela, Ben, and Claire will receive in terms of x:
A = 2x
B = x
C = 2x/5
To find the specific values of A, B, and C, we need to consider the total amount, which is £3.40. Since there are 100 pence in a pound, the total amount can be represented as 340p.
Now we can write an equation based on the given problem:
A + B + C = 340
Substituting the values we found earlier:
2x + x + 2x/5 = 340
Multiply the entire equation by 5 to get rid of the fraction:
10x + 5x + 2x = 340 * 5
Simplify the equation:
17x + 2x = 1700
Combine like terms:
19x = 1700
Divide both sides by 19 to solve for x:
x = 1700 / 19
x ≈ 89.47
Now we have the value of x, which represents Ben's share. Based on this, we can calculate the shares of Angela and Claire:
A = 2x ≈ 2 * 89.47 ≈ 178.94
C = 2x/5 ≈ 2 * 89.47/5 ≈ 35.79
Therefore, Angela will receive approximately £178.94, Ben will receive approximately £89.47, and Claire will receive approximately £35.79.