At a family reunion, each of Mateo's aunts and uncles is getting photographed once. The aunts are taking pictures in groups of 9 and the uncles are taking pictures in groups of 6. If Mateo has the same total number of aunts and uncles, what is the minimum number of aunts that Mateo must have?
Question
At a family reunion, each of Mateo's aunts and uncles is getting photographed once. The aunts are taking pictures in groups of 9 and the uncles are taking pictures in groups of 6. If Mateo has the same total number of aunts and uncles, what is the minimum number of aunts that Mateo must have?
Solution
Let's solve this problem step by step.
- Let's assume that Mateo has "x" aunts.
- Since the aunts are taking pictures in groups of 9, the total number of aunt groups can be calculated by dividing the number of aunts by 9: x/9.
- Similarly, let's assume that Mateo has "x" uncles.
- Since the uncles are taking pictures in groups of 6, the total number of uncle groups can be calculated by dividing the number of uncles by 6: x/6.
- According to the problem, the total number of aunt groups and uncle groups should be equal. So, we can set up the equation: x/9 = x/6.
- To solve this equation, we can cross-multiply: 6x = 9x.
- Subtracting 6x from both sides, we get: 3x = 0.
- Dividing both sides by 3, we find: x = 0.
Therefore, the minimum number of aunts that Mateo must have is 0.
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