Question

A jar contains 26 coins totaling $2.55 in nickels and dimes. How many dimes are in the jar?

Answer 1

25

Answer 2

Let's say that x = number of nickles, and y = number of dimes. One nickle is $0.05 and one dime is $0.10. Establish two equations with x and y:

x + y = 26

x*0.05 + y*0.10 = 2.55

From the first equation, let's find x:

x = 26 - y

Put this value into the second equation:

(26 - y)*0.05 + y*0.10 = 2.55

To makes things easier we can multiply both sides of the equation by 100:

(26 - y)*5 + y*10 = 255 ----->

130 - 5y + 10y = 255 ----->

5y = 125 -----> y = 125/5 -----> y = 25

So there are 25 dimes, which is your answer. To confirm the answer, notice again that x = 26 - y -----> x = 26 - 25 -----> x = 1

So there is only one nickle. We can confirm these answer by putting them into the second equation:

x*0.05 + y*0.10 = 2.55

1*0.05 + 25*0.10 = 2.55

0.05 + 2.5 = 2.55

2.55 = 2.55

Answer 3

let n = nickels
d = dimes

n+d = 26
5cn + 10cd = 255c

(c means cent)

systems...

-5n - 5d = -130
5n + 10d = 255

5d = 125
d = 25
n = 1