Question

2. 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 (9), while the earlier copper pennies weigh 3.11 g. A roll of pennies contains 50 coins. Suppose a particular roll of pennies weighs 132.32 g. A system of equations can be written to represent this context. To write a system of equations, consider the unknown variables of interest and the information given. a. What information is given about the roll of pennies? The number of pennies - Weight of pennies = 132.32g weight of 50 pennies 2. Write a two-equation system of equations representing this information, where x represents the number of pennies minted prior to 1983 in the roll and y represents the number of pennies minted after 1983 in the roll. x+y=50 3.11x +2.50y=132.32 C. Solve the system of equations using substitution. d. Interpret the solution.​

PLSSSS HELP MEEE

Answer 1

1) Information includes the weight of a roll of pennies (132.32 grams).2) Two equations are: x + y = 50 and 3.11x + 2.50y = 132.32. c) By setting up a system of linear equations where x and y represent the number of pre-1983 and post-1983 pennies respectively, and solving for y using substitution, we get the value of x=12 and y=38. d)we find there were 12 pre-1983 pennies and 38 post-1983 pennies in a roll weighing 132.32 grams.

Step-by-step explanation:

To solve this problem we first understand that we're dealing with a system of linear equations in two variables representing the number of two different types of pennies in a roll.

a) Given information includes the weight of a roll of pennies (132.32 grams), the weight of pre-1983 pennies (3.11 grams each), and the weight of post-1983 pennies (2.50 grams each). Also, there are 50 pennies in a roll.

b) The two equations representing this scenario are:

• The sum of the two types of pennies equals 50: x + y = 50
• The total weight of the pennies equals 132.32 grams: 3.11x + 2.50y = 132.32

c) To solve using substitution, first solve the first equation for x:

x = 50 - y

Then substitute that expression for x into the second equation:

3.11(50 - y) + 2.50y = 132.32

Now solve for y:

155.5 - 3.11y + 2.50y = 132.32

-0.61y = -23.18

y = 38

Now substitute y back into the first equation to find x:

x + 38 = 50

x = 12

d) The solution (x,y) indicates that there were 12 pre-1983 pennies and 38 post-1983 pennies in the roll.