Tyler puts all the coins in bags. Every bag has the same number of quarters and the same amount of dimes. How many bags of coins can Tyler make? How many quarters and how many dimes are in each bag?
To find the total number of coins, we can count the number of quarters and dimes separately and then find their least common multiple (LCM).
Let's say Tyler has Q quarters and D dimes.
We can create the following equation:
Q = D (the number of quarters is equal to the number of dimes)
The LCM of Q and D will give us the total number of coins.
Prime factorize Q:
Q = 2 * 2 * ... (Q factors)
Prime factorize D:
D = 2 * 2 * ... (D factors)
Since Q and D have the same prime factors, their LCM is simply Q itself.
So the total number of coins is Q.
Tyler can make bags of coins where each bag has Q quarters and Q dimes.
Therefore, Tyler can make Q bags of coins, and each bag has Q quarters and Q dimes.
To find the number of bags of coins Tyler can make, we need to determine the factors of both the total number of quarters and the total number of dimes.
Step 1: Let's assume Tyler has x quarters and x dimes.
Step 2: Since every bag has the same number of quarters and the same amount of dimes, the number of quarters and dimes must have a common factor.
Step 3: Prime factorize the number of quarters and number of dimes.
For example, if Tyler has 20 quarters and 20 dimes:
Number of quarters (20) = 2 * 2 * 5
Number of dimes (20) = 2 * 2 * 5
Step 4: Identify the common factors of both the number of quarters and number of dimes.
From the prime factorization, the common factors are: 2 and 5
Step 5: Determine the number of bags using either one of the common factors.
In this case, we can use either 2 or 5.
If we divide the number of quarters and dimes by 2:
20 quarters / 2 = 10
20 dimes / 2 = 10
So, Tyler can make 10 bags of coins, with each bag containing 10 quarters and 10 dimes.
Alternatively, if we divide the number of quarters and dimes by 5:
20 quarters / 5 = 4
20 dimes / 5 = 4
So, Tyler can also make 4 bags of coins, with each bag containing 4 quarters and 4 dimes.