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

Answer:

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

Step-by-step 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 $\frac{3}{5}$ of  Ali's money.

$b = \frac{3}{5}\cdot a$ (1)

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

$\frac{a}{c} = 4$ (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.