Jack had some pens for sale. He sold a total of 126 pens on Monday. On Tuesday, he sold 75% of the remaining pens. In the end, he was left with 10% of the pens he had at first. How many pens did he have at first?
Question
Jack had some pens for sale. He sold a total of 126 pens on Monday. On Tuesday, he sold 75% of the remaining pens. In the end, he was left with 10% of the pens he had at first. How many pens did he have at first?
Solution
Let's solve this step by step:
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Let's assume the total number of pens Jack had at first is X.
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On Monday, Jack sold 126 pens. So, the number of pens left after Monday is X - 126.
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On Tuesday, Jack sold 75% of the remaining pens. So, the number of pens left after Tuesday is 25% of (X - 126). This is because when he sells 75%, he is left with 25%.
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According to the problem, the number of pens left after Tuesday, which is 25% of (X - 126), is also 10% of the total number of pens Jack had at first. So, we can set up the following equation:
25% of (X - 126) = 10% of X
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To make it easier to solve, let's convert the percentages to decimals. So, the equation becomes:
0.25 * (X - 126) = 0.10 * X
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Distribute the 0.25 to both terms on the left side of the equation:
0.25X - 31.5 = 0.10X
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Rearrange the equation to get all terms involving X on one side:
0.25X - 0.10X = 31.5
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Simplify the left side:
0.15X = 31.5
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Solve for X by dividing both sides by 0.15:
X = 31.5 / 0.15
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X = 210
So, Jack had 210 pens at first.
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