Three friends got the prize money worth $231,000

.

The first friend would get four times

the amount of the third friend's portion. The third friend would get four times

the amount of the second friend's portion. Determine the amount that each friend would receive.

There are three unknowns in this problem. First, let's assign variables for these unknowns.

Let

x be the amount received by the first friend

y be the amount received by the second friend

z be the amount received by the third friend

Next, we formulate equations for the relationships

x = 4z

z = 4y

x + y + z = $231,000

Solving simultaneously,

4 (4y) + y + 4y = $231,000

21y = $231,000

y = $11,000

z = 4 ($11,000) = $44,000

x = 4 ($44,000) = $176,000