Question

99 points

These are the first sentences in the short story, "The Gift of the Magi," by O. Henry: "One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies."

A. Simplify the equation that represents the value of the coins. Make it an equation that expresses the value of quarters, dimes, and nickels.

B. Is it possible to have exactly 60 pennies in $1.87? Explain.

Answer 1

1.27 = .25q + .10d +.05n

No we cannot have exactly 60 pennies

Explanation:

Quarters = .25

Dimes = .10

Nickels = .05

Pennies = .01

Let q = quarters, d = dimes = n = nickels, p = pennies

One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies."

1.87 = .25q + .10d +.05n + .01p

But it says we have 60 pennies so replace p with 60

1.87 = .25q + .10d +.05n + .01(60)

1.87 = .25q + .10d +.05n + .60

Subtract .60 from each side

1.87-.6 = .25q + .10d +.05n + .60-.6

1.27 = .25q + .10d +.05n

Notice the 27cents

We need 2 pennies to get to 7 cents. We cannot have exactly 60 pennies and have 1.87