Question
The ratio of the number of Sam's books to Charlie's was 4:9 at first. Then, Sam bought 30 more books while Charlie gave away 15 books. In the end, the ratio of the number of Sam's books to Charlie's books was 5:3. How many books did Sam have at first?
Answers
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Let's start by setting up some equations to represent the given information.
Let S be the number of books Sam had at first, and let C be the number of books Charlie had at first. We know that:
S:C = 4:9
This means that Sam had 4x books and Charlie had 9x books, for some value of x.
After Sam bought 30 books, he had 4x + 30 books. And after Charlie gave away 15 books, he had 9x - 15 books. The ratio of Sam's books to Charlie's books at this point was:
(4x + 30):(9x - 15)
We're told that this ratio is 5:3, so we can set up another equation:
(4x + 30):(9x - 15) = 5:3
To solve for x, we can cross-multiply:
3(4x + 30) = 5(9x - 15)
Simplifying:
12x + 90 = 45x - 75
Subtracting 12x and adding 75 to both sides:
165 = 33x
x = 5
So at first, Sam had 4x books, or 4(5) = 20 books.
Let S be the number of books Sam had at first, and let C be the number of books Charlie had at first. We know that:
S:C = 4:9
This means that Sam had 4x books and Charlie had 9x books, for some value of x.
After Sam bought 30 books, he had 4x + 30 books. And after Charlie gave away 15 books, he had 9x - 15 books. The ratio of Sam's books to Charlie's books at this point was:
(4x + 30):(9x - 15)
We're told that this ratio is 5:3, so we can set up another equation:
(4x + 30):(9x - 15) = 5:3
To solve for x, we can cross-multiply:
3(4x + 30) = 5(9x - 15)
Simplifying:
12x + 90 = 45x - 75
Subtracting 12x and adding 75 to both sides:
165 = 33x
x = 5
So at first, Sam had 4x books, or 4(5) = 20 books.