Alyssa, Bart and Meghan are partners in a company in
which they share all profits
and losses in the ratio 5:3:2.
In one year, the profits were
$140 000. What is each
partner's share of the profit?

Hi,

Essentially, we are saying that Alyssa gets 5 parts of the whole thing (140,000), Bart gets 3 parts of the whole and Meghan gets 2 parts of the whole. The sum total of their parts = the whole. So now we need to find out how much one part is. Thus,"one part" should be the variable. Substitute p for "one part", so Alyssa gets 5p, Bart gets 3p, and Meghan gets 2p. Since the sum of the parts = the whole, your problem sets up as:  5p + 3p + 2p = 140,000  -->  10p = 140,000 --> 10p/10 = 140,000/10  -->  x = 14,000.

Alyssa gets 5p or (5 x 14,000)

Bart gets 3p or (3 x 14,000)

Meghan gets 2p or (2 x 14,000)

If the whole was a loss, it would be a negative, and instead of getting money, they would lose money.