Question

Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $438 million in ticket sales. If Singer B took in $22 million less than Singer A, how much did each tour generate?

Answer 1

To answer this question, we have that both singers generated $438 million in tickets sales.

Then, we can rewrite it in algebraic expressions as follows:

`A+B=438`

However, we know that singer B took in $22 million less than singer A:

`B=A-22`

Now, we can substitute this expression in the original one as follows:

`A+A-22=438`

And to solve this equation, we can add the like terms, and then add 22 to both sides of the equation as follows:

`2A-22+22=438+22\Rightarrow2A=460\Rightarrow(2A)/(2)=(460)/(2)`
`A=230`

Then, to find the earnings of singer B, we have:

`A+B=438\Rightarrow B=438-A`

Then, B is equal to:

`B=438-230\Rightarrow B=208`

Then, we can check that A + B is:

`A+B=230+208=438`

And we can see that singer B took in $22 million less than singer A:

`B=230-22=208`

In summary, therefore, we can say that each tour generated:

Singer A generated $230 million in ticket sales and Singer B generated $208 million.