Mrs Koh bought some pens, files and erasers. The ratio of the number of pens to the number of files to the number of erasers she bought was 1 : 2 : 3. The cost of each pen and eraser is $2.50 and $0.50 respectively. If she spent $60 on the pens and the erasers, how many files did she buy?
Say she bought x pens, 2x files, and 3x erasers. Adding up the cost of the pens and erasers, we have
2.50x + 0.50(3x) = 60.00
x = 15
So, she bought 30 files
To find out how many files Mrs. Koh bought, we need to analyze the information given. Let's break it down step by step:
1. Let's assign variables to the numbers of pens, files, and erasers. Let's say the number of pens is p, the number of files is f, and the number of erasers is e.
2. The ratio given is 1 : 2 : 3. This means that for every 1 pen, there are 2 files, and for every 2 files, there are 3 erasers.
3. Since we don't have the exact numbers for p, f, and e, let's express their values in terms of a common multiple. Let's assume the common multiple is 6. Therefore, the ratio becomes 1 x 6 : 2 x 6 : 3 x 6, which is 6 : 12 : 18.
4. Now that we have the ratio in terms of a common multiple, let's determine the cost of the pens and erasers. The cost of each pen is $2.50, so the total cost of all the pens is 6 x $2.50 = $15. The cost of each eraser is $0.50, so the total cost of all the erasers is 18 x $0.50 = $9. Therefore, the total cost of the pens and erasers is $15 + $9 = $24.
5. According to the information given, Mrs. Koh spent a total of $60 on the pens and erasers. So, we can set up an equation: $24 (cost of pens and erasers) + cost of files = $60.
Let's substitute the cost of files with a variable, c:
$24 + c = $60.
6. Now, solve the equation for c (cost of files):
c = $60 - $24 = $36.
7. Therefore, the cost of the files is $36.
8. However, we want to find the number of files Mrs. Koh bought, not the cost. Since the cost of each file is not provided, we can't determine the exact number of files.