80% of the people who signed up for a competition were adults. 70% of the children who signed up for the competition were boys. 60 more boys than girls signed up for the competition. After some more boys signed up for the competition, 25% of the people who signed up for the competition were boys. How many more boys signed up for the competition?
Question
80% of the people who signed up for a competition were adults. 70% of the children who signed up for the competition were boys. 60 more boys than girls signed up for the competition. After some more boys signed up for the competition, 25% of the people who signed up for the competition were boys. How many more boys signed up for the competition?
Solution
Let's break down the problem step by step:
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Let's denote the total number of people who signed up for the competition as T. According to the problem, 80% of T were adults, so 20% of T were children.
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Let's denote the number of children as C. According to the problem, 70% of the children were boys. So, the number of boys among the children is 0.7C.
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The problem also states that there were 60 more boys than girls. Since the total number of children is made up of boys and girls, we can write the equation: 0.7C (boys) = C - 60 (girls). Solving this equation for C, we get C = 200.
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So, initially, there were 0.7 * 200 = 140 boys.
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The problem then states that after some more boys signed up, 25% of the total number of people who signed up were boys. So, the number of boys after more signed up is 0.25T.
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The problem asks for how many more boys signed up. To find this, we subtract the initial number of boys from the final number of boys: 0.25T - 140.
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But we know from step 3 that T = 200 / 0.2 = 1000.
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Substituting T = 1000 into the equation from step 6, we get: 0.25*1000 - 140 = 250 - 140 = 110.
So, 110 more boys signed up for the competition.
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