If Luis has 16 dimes and nickels in his pocket, and they have a combined value of 115 cents, how many of each coin does he have?

Answer 1

Let d = the number of dimes

and n = the number of nickels

From the problem we know that there are 16 coins total in his pocket, so we can create the following equation:

d + n = 16

We also know that dimes are worth 10 cents and nickels are 5 cents. So the total amount of money can be represented by multiplying d (the number of dimes) by 10 and multiplying n (the number of nickels) by 5. The problem states that the total amount combines to 115 cents. So we can create this second equation:

10d + 5n = 115

Now that we have these two equations, we can solve for n and d using either the Substitution method or the Elimination method.

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*UPDATE: How to solve using the Substitution Method

d + n = 16

10d + 5n = 115

Solve the first equation for d by subtracting n from both sides of the equation:

d = 16 - n

10d + 5n = 115

Substitute the first equation into the second equation:

10(16 - n) + 5n = 115

Distribute the 10 and then solve for n:

10(16 - n) + 5n = 115

160 - 10n +5n = 115

160 - 5n = 115

-5n = 115 - 160

-5n = -45

n = 9

Now to solve for d, we can substitute the value we got for n into either of the two equations (the first equation looks a lot simpler so I'll do that one):

d + n = 16

d + (9) = 16

d = 16 - 9

d = 7