Question

Miles has 25 coins in his pocket. Some are nickels and some are dimes. He has a total of $1.65. How many of each type of coin does he have? Let x represent _____________________________ Let y represent _____________________________ System: _____________________ _____________________ Solution: x = ____________ y = ____________

Answer 1

Answer: 17 nickels, and 8 dimes.

Explanation:

So Miles has 25 coins in his pocket, Suppose that x is the number of nickels, and y is the number of dimes, then we have that:

x + y = 25

And we also know that the total value is $1.65

Then we have that:

x*0.05 + y*0.10 = 1.65

Then we have a system of equations:

x + y = 25

x*0.05 + y*0.10 = 1.65

The first step is isolating one of the variables in one of the equations, i will isolate x in the first one.

x = 25 - y

Now we can replace that in the second equation:

(25 - y)*0.05 + y*0.10 = 1.65

Now we solve this for y.

25*0.05 - y*0.05 + y*0.10 = 1.65

1.25 + y*(0.10 - 0.05) = 1.65

y*0.05 = 1.65 - 1.25 = 0.40

y = 0.40/0.05 = 8

So Miles has 8 dimes.

And:

x + y = 25

x + 8 = 25

x = 25 - 8 = 17

And Miles has 17 nickels.