Ludek has 22 coins in his pocket. The coins have a total value of $1.45. if the coins are nickels and dimes only, how many of each coin does ludek have?

Question

22 coins make up a $1.45.

 

If the coins are nickels and dimes only how many does ludek have

Answer 1

Hello Sarah,

 

We need to set up 2 equations to solve this problem. The first thing we need to do is to assign variables to the unknown amounts. Let the question guide you. Since it's asking for how many nickels and dimes, let's let nickels = n and dimes = d. Now, our first equation is always about the number of coins we have. Since nickels + dimes = 22 our equation would be n+d=22. The second equation always deals with the value of the coins. Since nickels are worth .05 and dimes are worth .10, our equation would look like .05n+.10d=1.45. Now that we have 2 equations with 2 unknowns we can use substitution or elimination to solve the equations. I think substitution would be the simplest in this situation.

 

So we solve the first equation for a variable.

n + d = 22

or d = 22 - n

 

Now we can substitute that in place of d in the second equation.

.05n + .10d = 1.45

so .05n + .10(22-n) = 1.45

now distribute to get .05n + 2.2 - .10n = 1.45

combine like terms to get -.05n + 2.2 = 1.45

move the 2.2 to the right by subtracting from both sides to get -.05n = -.75

Now divide both sides by -.05 to get n = 15

 

Since n + d = 22 and we now know n = 15 we can find d.

15 + d = 22

or d = 7

 

I hope this has helped and if I can help to tutor you in the future please let me know.