Museum employees are preparing an exhibit of ancient coins. They have 49 copper coins and 35 silver coins to arrange on shelves. Each shelf will have the same number of copper coins and same number of silver coins. How many shelves will the employees need for this exhibit?
(HOW IS THIS POSSIBLE???)
Both 49 and 35 are evenly divisible by 7. So 7 shelves must be needed.
Each shelf will contain 7 copper coins and 5 silver coins.
Thanks so much! :D
You're welcome, Amber.
To determine the number of shelves needed for the exhibit, we need to find the greatest common divisor (GCD) of the number of copper coins and the number of silver coins.
In this case, we have 49 copper coins and 35 silver coins. The GCD of these two numbers will give us the maximum number of shelves that can be arranged evenly.
To find the GCD, we can use the Euclidean algorithm. The Euclidean algorithm states that the greatest common divisor of two numbers can be found by repeatedly subtracting the smaller number from the larger number until one of them becomes zero. The remaining non-zero number will be the GCD.
Let's apply the Euclidean algorithm to find the GCD of 49 and 35:
Step 1: Subtract the smaller number (35) from the larger number (49):
49 - 35 = 14
Step 2: Repeat step 1, but now the larger number becomes 35 and the smaller number becomes 14:
35 - 14 = 21
Step 3: Repeat step 1 once more:
21 - 14 = 7
Step 4: Repeat step 1:
14 - 7 = 7
Step 5: Repeat step 1 again:
7 - 7 = 0
Since one of the numbers has become zero, we stop the process. The remaining non-zero number is the GCD.
In this case, the GCD of 49 and 35 is 7.
Therefore, the museum employees will need 7 shelves for this exhibit because each shelf will have the same number of copper coins (49 / 7 = 7) and the same number of silver coins (35 / 7 = 5).