Question

In 1983 the composition of pennies in the United States was changed due, in part, to the rising cost of copper. Pennies minted after 1983 weigh 2.50 grams while the earlier copper pennies weigh 3.11 grams. a. A roll of pennies contains 50 pennies. If a particular roll of pennies weighs 138.42 grams, how many of the earlier copper pennies and how many of the after 1983 pennies does this roll contain? b. Suppose you measure a roll of pennies on a scale which only reads the weight to the nearest gram. The scale says that the roll of pennies weighs 131 grams. What can you conclude about the pennies in this roll? What if the roll weights 134 grams? Explain.

Answer 1

Answer:

Solution for (a)

Earlier Copper pennies are 22.

After 1983 pennies are 28.

Step-by-step explanation:

Pennies minted after 1983 weigh 2.50g

Earlier copper pennies weigh 3.11g

A roll of pennies contains 50 pennies.

A particular roll of pennies weighs 138.42g

Let the number of pennies minted after 1983 be x and;

Earlier copper pennies be 50 - x

2.50x + 3.11(50 - x) = 138.42

Opening the brackets gives;

2.5x + 155.5 - 3.11x = 138.42

Solving like terms together gives;

-0.61x = -17.08

Dividing through gives;

x = 28

So there are 28 after 1983 pennies and;

50 - 28 = 22 earlier pennies.