A shop sells pens and files only in packs. A pack of 7 pens cost $28. A pack of 6 files cost $30. A student wants to buy an equal number of pens and files. What is the least amount that the student must pay?
Question
A shop sells pens and files only in packs. A pack of 7 pens cost 30. A student wants to buy an equal number of pens and files. What is the least amount that the student must pay?
Solution
To solve this problem, we first need to find the cost of one pen and one file.
- The cost of one pen is 4.
- The cost of one file is 5.
However, the student wants to buy an equal number of pens and files, and the shop only sells these items in packs. Therefore, we need to find the least common multiple (LCM) of the number of items in a pack, which is 7 (for pens) and 6 (for files).
The LCM of 7 and 6 is 42. This means the student needs to buy 6 packs of pens and 7 packs of files.
- The cost for 6 packs of pens is 6 * 168.
- The cost for 7 packs of files is 7 * 210.
Therefore, the least amount that the student must pay is 210 = $378.
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