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.
[tex]a[/tex] - Ali's money.
[tex]b[/tex] - Bryan's money.
[tex]c[/tex] - Carrie's money.
(ii) Bryan's money was [tex]\frac{3}{5}[/tex] of Ali's money.
[tex]b = \frac{3}{5}\cdot a[/tex] (1)
(iii) The ratio of Ali's money to Carrie's money was 4 : 1.
[tex]\frac{a}{c} = 4[/tex] (2)
(iv) Ali had $ 160 more than Bryan.
[tex]a = b + 160[/tex] (3)
After some algebraic handling, we have the following system of linear equations:
[tex]3\cdot a - 5 \cdot b = 0[/tex] (1b)
[tex]a - 4\cdot c = 0[/tex] (2b)
[tex]a - b = 160[/tex] (3b)
The solution of the system is: [tex]a = 400[/tex], [tex]b = 240[/tex], [tex]c = 100[/tex]
The sum of money is:
[tex]s = a + b + c[/tex]
[tex]s = 740[/tex]
The sum of money received by Ali, Carrie and Bryan is $ 740.
