Question

Pete and Mike were competing at soccer to see who could score the most number of goals in total. In today's match, Pete managed to score 4 goals, and Pete and Mike's scores were in the ratio of 1 : 2. Before today's match, the scores for Pete and Mike were in the ratio of 1 : 3. Mike did not manage to score any goal today. How many goals did Mike score in total?

Answer 1

1x + 4 : 2x = 1 : 2

We can cross-multiply to get:

2(1x + 4) = 1(2x)

2x + 8 = 2x

8 = 2x - 2x

8 = 0

This is not possible, so our assumption that Pete and Mike's scores before today's match were 1x and 3x respectively must be incorrect.

Let's try a different assumption. Let's assume that before today's match, Pete and Mike's scores were 2x and 6x respectively. After today's match, Pete scored 4 goals, so his total score is now 2x + 4. We also know that Pete and Mike's scores were in the ratio of 1:2 after today's match. Therefore, we can write:

2x + 4 : 2(6x) = 1 : 2

We can simplify this to:

2x + 4 : 12x = 1 : 2

We can cross-multiply to get:

2(2x + 4) = 1(12x)

4x + 8 = 12x

8 = 12x - 4x

8 = 8x

x = 1

Therefore, before today's match, Pete and Mike's scores were 2 and 6 respectively. After today's match, Pete's score is 2 + 4 = 6. Since Pete and Mike's scores were in the ratio of 1:2 after today's match, Mike's score must be twice that of Pete's score, which is 2 x 2 = 4.

Therefore, Mike's total score is 6 + 4 = 10. Mike scored a total of 10 goals.