Question

The winner and runner-up of a TV music contest had lucrative earnings immediately after the show's finale. The runner-up earned $1 million less than half of the winner's earnings. If their combined earnings totaled $10 million, how much did each person make?

Answer 1

The winner earned approximately $7.33 million, and the runner-up earned approximately $2.67 million.

Step-by-step explanation:

Let's denote the amount of money the winner earned as 'W' and the amount of money the runner-up earned as 'R'. From the given information, we form two equations. The first equation, from the statement that the runner-up earned $1 million less than half the winner's earnings, is :

R = W/2 - 1.

The second equation, that their combined earnings totaled $10 million, is W + R = 10. We solve these equations to get the answer.

Substituting R in the second equation gives:

W + W/2 - 1 = 10.

Multiplying through by 2 to eliminate the fraction gives:

2W + W - 2 = 20.

Simplifying gives: 3W = 22. So W, the winner's earnings, is approximately $7.33 million. Substituting W in the first equation gives:

R = 7.33/2 - 1 = $2.67 million, approximately.

Therefore, the winner earned around $7.33 million and the runner-up earned around $2.67 million.

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