Ratio and Proportion: Question 2

Worked solution

Part (a)

The investments are in the ratio $\text{Amara} : \text{Bilal} : \text{Chen} = 8 : 5 : 3.$

Use the known difference. Amara has $8$ parts and Chen has $3$ parts, so the difference between their investments is $8 - 3 = 5 \text{ parts}.$

We are told this difference equals $240, so

$5 \text{ parts} = 240.$

Find the value of one part: $1 \text{ part} = \frac{240}{5} = 48.$

So each part is worth $48.

Find the total. The total number of parts is $8 + 5 + 3 = 16,$ so the total investment is $16 \times 48 = 768.$

The three friends invest a total of $\boxed{768}$ dollars.

Find each share:

$\text{Amara} = 8 \times 48 = 384,$ $\text{Bilal} = 5 \times 48 = 240,$ $\text{Chen} = 3 \times 48 = 144.$

Check: $384 + 240 + 144 = 768$ ✓, and $384 - 144 = 240$ ✓.

So Amara invests $384, Bilal invests $240 and Chen invests $144.

Part (b)

The profit is shared in the same ratio $8 : 5 : 3$, but the amounts are different, so we must work out a new value for one part.

Bilal’s share is $5$ parts, and this equals $450: $5 \text{ parts} = 450.$

Value of one part: $1 \text{ part} = \frac{450}{5} = 90.$

Total profit has $8 + 5 + 3 = 16$ parts: $16 \times 90 = 1440.$

The total profit is $\boxed{1440}$ dollars, i.e. $1,440.

Check: Amara $= 8 \times 90 = 720$, Chen $= 3 \times 90 = 270$, and $720 + 450 + 270 = 1440$ ✓.