Question

A family owns two businesses that made a combined profit of $$$10 million in the previous financial year, with business B making $$4 times as much profit as business A. Let $$x and $$y be the profits ( in millions) of business A and business B respectively. 2a Use the fact that the two businesses made a combined profit of $$$10 million to set up an equation involving $$x

Answer 1

The equation to find the profit made by business combined is
`x+4x = 10`.

Business A made $2 million profit and Business B made $8 million profit.

Explanation:

Given:

Profit made in previous financial year = $10 million

We need to write an equation to find the profit made by the business.

Solution:

Let the profit (in millions) made by business A be 'x'.

Let the profit (in millions) made by business B be 'y'.

Now given:

business B making 4 times as much profit as business A.

so we can say that;

`y =4x`

Now we know that;

Profit made in previous financial year is equal to sum of profit (in millions) made by business A and profit (in millions) made by business B.

framing in equation form we get;

`x+y =10\ million`

Substituting the value of y in above equation we get;

`x+4x = 10`

Hence The equation to find the profit made by business combined is
`x+4x = 10`.

On Solving above equation we get;

`5x =10\\\\x =(10)/(5) = \$2 \ million`

profit (in millions) made by business A =
`\$2 \ million`

profit (in millions) made by business B =
`4x =4* 2 =\$8 \ million`

Hence Business A made $2 million profit and Business B made $8 million profit.