At Mrs. Livingston's favorite grocery store, oranges are sold in bags of 10 and grapefruits are sold in bags of 6. Mrs. Livingston wants to buy an equal number of oranges and grapefruits.
What is the smallest number of each fruit Mrs. Livingston needs to buy in order to have an equal number of oranges and grapefruits?
a.12
b.20
c.30
d.60
The easy way is to take the answers and see if they are divisible by 10 and 6 to give a whole number (since the two fruits are sold by bags and not apiece).
12, not divisible by 10.
20, not divisible by 6.
30, divisible by 10 and 6.
60, divisible by 10 and 6.
To check ourself, 30 oranges can be bought in 30/10 = 3 bags and 30 grapefruit can be bought in 30/6 = 5 bags.
60 oranges can be bought in 60/10 = 6 bags while 60 grapefruit can be bought in 60/6=10 bags.
But the answer is 30 fruit since that is smaller than 60.
Thank you SOOOO much!
I need to explain how i got theese prices.
To find the smallest number of each fruit Mrs. Livingston needs to buy, we need to find the least common multiple (LCM) of 10 and 6. The LCM is the smallest number that is divisible by both numbers.
To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
From the lists, we can see that 30 is the smallest number that appears in both lists. Therefore, the smallest number of each fruit Mrs. Livingston needs to buy is 30.
Now we need to check which option from the answers (a, b, c, d) is equal to 30:
a. 12 - not equal to 30
b. 20 - not equal to 30
c. 30 - equal to 30
d. 60 - not equal to 30
Therefore, the correct answer is c. 30.