Question

Ali, Carrie and Bryan received a sum of money. Bryan's money was 3/5 as much as Ali's money. The ratio of Ali's money to Carrie's money was 4:1. Ali had $160 more than Bryan. How much was the sum of money.

Answer 1

The sum of money received by Ali, Carrie and Bryan is $ 740.

Explanation:

At first we translate mathematically each sentence:

(i) Ali, Carrie and Bryan received a sum of money.

`a` - Ali's money.

`b` - Bryan's money.

`c` - Carrie's money.

(ii) Bryan's money was
`(3)/(5)` of Ali's money.

`b = (3)/(5)\cdot a` (1)

(iii) The ratio of Ali's money to Carrie's money was 4 : 1.

`(a)/(c) = 4` (2)

(iv) Ali had $ 160 more than Bryan.

`a = b + 160` (3)

After some algebraic handling, we have the following system of linear equations:

`3\cdot a - 5 \cdot b = 0` (1b)

`a - 4\cdot c = 0` (2b)

`a - b = 160` (3b)

The solution of the system is:
`a = 400`,
`b = 240`,
`c = 100`

The sum of money is:

`s = a + b + c`

`s = 740`

The sum of money received by Ali, Carrie and Bryan is $ 740.