If a penny prior to 1982 weighted 3.1 grams and a current one weighs 2.5 grams how many pennies weighing 3.1 and 2.5 will I need in a combination of ten in total to have 25 grams??
x + y = 10
3.1 x + 2.5 y = 25
solves easily by inspection (observation)
Thanks , that's exactlywhat I thought, but did something wrong when solving and thought I was wrong .
THANKS!!
To determine the combination of pennies weighing 3.1 grams and 2.5 grams that will add up to a total weight of 25 grams, we can set up a system of equations.
Let's assume the number of pennies weighing 3.1 grams is x, and the number of pennies weighing 2.5 grams is y.
Since each penny prior to 1982 weighs 3.1 grams, the total weight contributed by these pennies would be 3.1x grams.
Similarly, if each current penny weighs 2.5 grams, the total weight contributed by these pennies would be 2.5y grams.
According to the problem, the total weight needs to be 25 grams. Therefore, we can write the equation:
3.1x + 2.5y = 25
However, we also have another constraint, which is the total number of pennies must be 10:
x + y = 10
Now, we have a system of two equations:
3.1x + 2.5y = 25
x + y = 10
We can use algebraic methods such as substitution or elimination to solve this system of equations. Let's use the substitution method for this example:
First, solve the second equation for x:
x = 10 - y
Now substitute this into the first equation:
3.1(10 - y) + 2.5y = 25
31 - 3.1y + 2.5y = 25
31 - 0.6y = 25
Next, isolate y:
-0.6y = 25 - 31
-0.6y = -6
y = (-6) / (-0.6)
y = 10
Now substitute the value of y back into the second equation to find x:
x + 10 = 10
x = 10 - 10
x = 0
Therefore, we would need 0 pennies weighing 3.1 grams and 10 pennies weighing 2.5 grams to have a total weight of 25 grams when combining a total of 10 pennies.