Question

In a cricket match, Emma scored 5 fewer runs than Alex, and Alex scored three times as many runs as Toni. Between them they scored 93 runs. How many runs did each player score?

The Answer from the Book was.
Emma Scored 37 Runs.
Alex Scored 42 Runs.
Toni Scored 14 Runs.

I NEED HELP ASAP!!!!!

Answer 1

Explanation:

Emma = Alex - 5

Alex = Toni × 3

therefore,

Toni = Alex / 3

Emma + Alex + Tony = 93

so, let's use the first two equations (identities) in the last big one, so that we have actually only one variable (Alex).

once we solve that, we can get the other two values out of the first 2 equations.

(Alex - 5) + Alex + (Alex/3) = 93

let's multiply everything by 3 to get rid of the fraction :

3(Alex - 5) + 3×Alex + 3(Alex/3) = 3×93

3×Alex - 15 + 3×Alex + Alex = 279

7×Alex - 15 = 279

7×Alex = 294

Alex = 294/7 = 42 runs.

Emma = Alex - 5 = 42 - 5 = 37 runs.

Toni = Alex/3 = 42/3 = 14 runs.