A bookstore sold pens and markers. The ratio of pens to markers was 1 : 4 at first. The store owner bought some more pens and markers to make the total to 62 . Now there were 3 times as many pens as the original quantity, and 7 times as many markers as the original quantity. How many pens were there in the end?
Question
A bookstore sold pens and markers. The ratio of pens to markers was 1 : 4 at first. The store owner bought some more pens and markers to make the total to 62 . Now there were 3 times as many pens as the original quantity, and 7 times as many markers as the original quantity. How many pens were there in the end?
Solution
Let's denote the original number of pens as P and the original number of markers as M.
From the problem, we know that the ratio of pens to markers was 1:4 at first. So, we can write this as P/M = 1/4, or P = M/4.
We also know that the store owner bought more pens and markers to make the total 62. Now there were 3 times as many pens as the original quantity, and 7 times as many markers as the original quantity. So, we can write this as 3P + 7M = 62.
Substituting P = M/4 into the second equation gives us 3(M/4) + 7M = 62, or 3M/4 + 7M = 62. Multiplying through by 4 to clear the fraction gives us 3M + 28M = 248, or 31M = 248. Dividing both sides by 31 gives us M = 8.
Substituting M = 8 back into P = M/4 gives us P = 8/4 = 2.
So, the original number of pens was 2 and the original number of markers was 8.
In the end, there were 3 times as many pens as the original quantity, so there were 3*2 = 6 pens.
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