[Solved] John buys some boxes of pencils and some packets of pens for people to use at a conference. There are 40 pencils in a box. There are 15 pens in a packet. John gives one pencil and one pen to each person at a conference. He has no pencils or pens left. How many boxes of pencils and how many packets of pens did John buy?
John buys some boxes of pencils and some packets of pens for people to use at a conference. There are 40 pencils in a box. There are 15 pens in a packet. John gives one pencil and one pen to each person at a conference. He has no pencils or pens left. How many boxes of pencils and how many packets of pens did John buy?
Concept used
We will use the concept of Least Common Multiple LCM to solve the given problem.
Solution: Number of pencils in a box = 40
Number of pens in a packet = 15
We have to find the number of boxes of pencils and pens John brought
We will use the least common multiple so that number of pencils and pens becomes equal.
LCM of 40, 15 = 5 × 3 × 2 × 2 × 2
LCM of 40, 15 = 120
⟹Number of pencils John buys = 3
Hence, John buys 2 boxes of pencils.
⟹Number of pens John buys = 8
Hence, John buys 8 boxes of pens.
Conclusion
John buys some boxes of pencils and some packets of pens for people to use at a conference. There are 40 pencils in a box. There are 15 pens in a packet. John gives one pencil and one pen to each person at a conference. He has no pencils or pens left. John buys 2 boxes of pencils and 8 boxes of pens.