Gabby has 130 insects in her bug collection that have wings and 70 that have pincers. She wants to buy display cases for her collection. Each display cases should have an equal number of insects with wings and pincers. If she wants each display case to have the greatest number of insects, how many display cases does she need to buy?
How many with wings in each container?
what is 130 minus 70?
To determine the number of display cases Gabby needs to buy, we first need to find the greatest common divisor (GCD) of the number of insects with wings and the number of insects with pincers.
In this scenario, Gabby has 130 insects with wings and 70 insects with pincers. To find the GCD, we can use the Euclidean algorithm.
Step 1: Divide the larger number (130) by the smaller number (70) and find the remainder.
130 / 70 = 1 remainder 60
Step 2: Divide the smaller number (70) by the remainder (60) and find the new remainder.
70 / 60 = 1 remainder 10
Step 3: Repeat this process until the remainder becomes 0.
60 / 10 = 6 remainder 0
Since the remainder has become 0, the last non-zero remainder (10) is the GCD of 130 and 70.
Therefore, the GCD of 130 and 70 is 10.
Now, to determine the number of display cases Gabby needs to buy, we divide the total number of insects with wings or pincers (130 + 70 = 200) by the GCD (10).
Number of display cases = Total number of insects / GCD
= 200 / 10
= 20
Therefore, Gabby needs to buy 20 display cases. Each display case will have an equal number of insects with wings and pincers.
Now, to answer your second question, since each display case has an equal number of insects with wings and pincers, we divide the total number of insects with wings by the number of display cases.
Number of insects with wings in each container = Total number of insects with wings / Number of display cases
= 130 / 20
= 6.5
However, since we cannot have a fraction of an insect in a display case, we need to round up the number to the nearest whole number.
Therefore, each display case should have 7 insects with wings.