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.

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

No we cannot have exactly 60 pennies

Step-by-step 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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!