Question

Mary and Mike enter invest $700 and $300 in a partnership. They divided their profits as follows: `1/3` is divided equally the remainder is split according to the investments. If Mary received $800 more than Mike, what was the profit made by the business?

Answer 1

business profit: `$1500`

Explanation:

Mary's share of the investments is
`color(white)("XXX")($300)/($700+$300) = 3/10 (or 30%)`

Let the business profit be `p`

According to the information given,
Mary should receive
`color(white)("XXX")1/3xxp+ 30%*(2/3xxp)`

`color(white)("XXX")=100/300p+60/300p`

`color(white)("XXX")=160/300p`

We are also told that Mary received $800#

So
`color(white)("XXX")160/300p=$800`

`color(white)("XXX")rArr p =($800xx300)/160 = $(5xx300)=$1500`