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?
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?
Solution
Let's break this down:
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Today, Pete scored 4 goals. The ratio of Pete's to Mike's scores today was 1:2. Since Mike didn't score any goals today, this means that the 4 goals Pete scored today were enough to make his total score half of Mike's total score.
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Before today's match, the scores for Pete and Mike were in the ratio of 1:3. This means that for every goal Pete had, Mike had 3.
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Now, we need to find out how many goals Mike scored in total. Since Pete's 4 goals today made his total score half of Mike's total score, this means that before today's match, Pete must have had half as many goals as he has now, which is 2 goals.
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Since the ratio of Pete's to Mike's scores before today's match was 1:3, this means that Mike must have had 3 times as many goals as Pete had before today's match, which is 3 * 2 = 6 goals.
So, Mike scored 6 goals in total.
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