Pencils come in packs of six. Erasers come in packs of eight. Aron wants to purchase pencils and erasers such that he has exactly one eraser per pencil. i. What is the minimum number of pencils or erasers he can buy? ________ ii. What is the smallest number of packages of pencils and erasers Aron should buy? Pencil packs = _______ Eraser Packs = _______
Answers
Answer:
i) Pencils- 6
Erasers - 8
ii) 1and 1
Aron should buy 4 pack of pencils and 3 pack of erasers so that he has exactly one eraser per pencil
The minimum number of pencils or erasers he can buy is 24
Solution:
Given that,
Pencils come in packs of six
Which means,
Each pack = 6 pencils
Erasers come in a pack of eight
Which means,
Each pack = 8 erasers
Aron wants to purchase pencils and erasers such that he has exactly one eraser per pencil
Which means,
Number of pencils is equal to number of erasers
We need to find how many packs would satisfy this situation
Find the LCM of 6 and 8
List all prime factors for each number.
Prime Factorization of 6 is: 2 x 3
Prime Factorization of 8 is: 2 x 2 x 2
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list
2, 2, 2, 3
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 = 24
Thus,
Pack of pencils = 24/6 = 4
Pack of erasers = 24/8 = 3
The minimum number of pencils or erasers he can buy is 24
Thus, Aron should buy 4 pack of pencils and 3 pack of erasers so that he has exactly one eraser per pencil
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