One penny has a mass of 2.5 g. Each roll of pennies contains 50 pennies. Write an equation with two variables that can be used to determine the total mass in grams of the pennies in any number of rolls of pennies. Show your work.
Let's assume that the number of rolls of pennies is represented by the variable "r" and the total mass of the pennies in grams is represented by the variable "m".
We know that each roll contains 50 pennies, and the mass of each penny is 2.5 grams. Therefore, the mass of one roll of pennies can be calculated by multiplying the mass of one penny by the number of pennies in a roll, which gives us:
Mass of one roll = 2.5 grams/penny * 50 pennies/roll
Now, since we want to determine the total mass of the pennies in any number of rolls, we can express this using the variables "m" (total mass) and "r" (number of rolls):
Total mass = Mass of one roll * Number of rolls
Therefore, the equation with two variables that can be used to determine the total mass in grams of the pennies in any number of rolls of pennies is:
m = (2.5 grams/penny * 50 pennies/roll) * r
Simplifying the equation:
m = 125 grams/roll * r
Hence, the equation is m = 125r, where "m" represents the total mass in grams and "r" represents the number of rolls of pennies.
To determine the total mass of pennies in any number of rolls, we can use the equation:
Total Mass = Mass per Penny × Number of Pennies
Let's break it down step by step:
1. Define the variables:
Let's use the variables:
- T for Total Mass
- M for Mass per Penny
- N for Number of Pennies in a roll
2. Identify the given information:
From the problem, we know that:
- Mass per Penny (M) = 2.5 grams
- Number of Pennies in a roll (N) = 50 pennies
3. Write the equation:
Using the variables and the given information, the equation becomes:
T = M × N
4. Substitute the given values:
Now we substitute the known values into the equation:
T = 2.5 × 50
5. Evaluate the equation:
Perform the multiplication to find the total mass of pennies:
T = 125 grams
So, the equation to find the total mass of pennies in any number of rolls is:
Total Mass (T) = Mass per Penny (M) × Number of Pennies (N)
T = 2.5 × N
By substituting the value of N with the actual number of pennies in a roll, you can easily calculate the total mass in grams of any number of rolls of pennies.