Jason has 12 pens and 30 pencils. He wants to distribute the pens and pencils into groups, with each group having the same ratio of pens to pencils. How many groups like these can be created?
Question
Jason has 12 pens and 30 pencils. He wants to distribute the pens and pencils into groups, with each group having the same ratio of pens to pencils. How many groups like these can be created?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of pens and pencils Jason has. The GCD will tell us the largest number of groups Jason can create where each group has the same ratio of pens to pencils.
Step 1: Find the GCD of 12 (pens) and 30 (pencils).
The factors of 12 are: 1, 2, 3, 4, 6, 12. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
The greatest number that is a factor of both 12 and 30 is 6.
Step 2: Divide the number of pens and pencils by the GCD.
12 pens ÷ 6 = 2 pens per group. 30 pencils ÷ 6 = 5 pencils per group.
So, Jason can create 6 groups, with each group containing 2 pens and 5 pencils.
Similar Questions
Mr. Kaur is putting together activity packs for his class. He has 42 pencils and 7 colouring books and wants to create identical activity packs with the same ratio of pencils to colouring books.Given that there must be at least one colouring book per pack, how many pencils will be in each pack?
A family is preparing backpacks filled with school supplies to donate to children in need. They have 12 pencils and 16 notebooks. If they want to make all the backpacks the same, with no school supplies left over, what is the greatest number of backpacks they can fill?
The ratio of pencils to pens is 6:7Given that there are 65 pencils and pens in total, calculate how many pencils there are.
A bookstore sold pens and markers. The ratio of pens to markers was 1 : 4 at first. The store owner bought some more pens and markers to make the total to 62 . Now there were 3 times as many pens as the original quantity, and 7 times as many markers as the original quantity. How many pens were there in the end?
A pencil case contains pens, pencils and crayons.The ratio of pens to pencils is 10𝑛:9.The ratio of pencils to crayons is 10:9𝑛.Work out the ratio of pens to crayons.Give your answer in its simplest form.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.