Question

A company offers a nut mixture with 7 peanuts for every 3 almonds. The company changes the mixture to have 9 peanuts for every 5 almonds, but the number of nuts per container does not change.

Plsssss help i'm so stuck :(

a. How many nuts are in the smallest possible container?

Answer 1

70

Explanation:

Nut mixture 1: 7 peanuts for every 3 almonds.

Therefore, the container has to hold nuts in multiples of 10, since 7+3=10 and 7 is not divisible by 3.

Nut mixture 2: 9 peanuts for every 5 almonds.

Therefore, the container has to hold nuts in multiples of 14, since 9+5=14 and 9 is not divisible by 5.

To find the number of nuts in the smallest possible container, find the least common multiple (LCM) of 10 and 14.

To find the LCM, list the multiples of each number and locate the smallest multiple that is exactly divisible by both the numbers:

• Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
• Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...

Therefore, the LCM of 10 and 14 is 70.

So there are 70 nuts in the smallest possible container.