Question

Angela and Michelle shared some money in the ratio 4: 9 then Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20. Work out how much money was originally shared.​

Answer 1

Using a system of equations, it is found that £52 was originally shared.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

• Variable x: Angela's share.

• Variable y: Michelle's share.

• Variable z: Daniel's share.

Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:

• $x = \frac{4t}{13}$.

• $y = \frac{9t}{13}$

Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:

$\frac{x}{2} + \frac{y}{3} = 20$

$\frac{4t}{26} + \frac{9t}{39} = 20$

$\frac{12t + 18t}{78} = 20$

30t = 20 x 78

t = 20 x 78/30

t = £52.

More can be learned about a system of equations at brainly.com/question/24342899

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