SOLUTION: A student weighs 885 pennies and finds them to have a mass of 2500.4g. If the pre-1982 pennies weigh an average 3.09g and the post-1982 pennies weigh 2.51 g. How many of pennies ar

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Question 503698: A student weighs 885 pennies and finds them to have a mass of 2500.4g. If the pre-1982 pennies weigh an average 3.09g and the post-1982 pennies weigh 2.51 g. How many of pennies are pre-1982
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
X = count of old pennies
3.09*X = weight of old pennies
.
Y = count of new pennies
2.51*Y = weight of new pennies
.
X+Y = 885 pennies
Y = 885-X
.
3.09*X + 2.51*Y = 2500.4
.
multiply by 100 to remove decimals
.
309X + 251Y = 250040
.
substitute for Y = 885-X
.
309X + 251(885-X) = 250040
.
309X + 222135 -251X = 250040
309X -251X = 250040 - 222135
58X = 27905
.
X = 481.12
.
Recall, we do not have counts but instead have average weights.
So having a result that is not an integer is to be expected.
We can assume X = 481.
.
That means
Y = 885 - 481
Y = 404
.
Always check your work.
3.09 * 481 = 1486.29
2.51 * 404 = 1014.04
1486.29+1014.04 = 2500.33
Compared to 2500.4, it's close.
.
Answer: There were 481 older pennies and 404 newer pennies.