Question

Alexandra has $2.10 worth of nickels and dimes. She has a total of 27 nickels and dimes all together. Determine the number of nickels and dimes that Alexandra has by writing and solving a system of equations. I need to use substitution or elimination to solve this.

Answer 1

• 15 dimes
• 12 nickels

Explanation:

Let n and d represent the number of nickels and dimes, respectively. The given information can be used to write two equations:

0.05n + 0.10d = 2.10 . . . . . . the value of the coins

n + d = 27 . . . . . . . . . . . . . . . the number of the coins

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In "mixture" problems like this, it is usually convenient to solve for the variable representing the highest-value contributor to the mix. Here, that would be the number of dimes. So, we want to eliminate n from the equation we're solving. We can do that by writing an expression for n, then using substitution.

From the second equation, ...

n = 27 -d

Substituting into the first equation, we get ...

0.05(27 -d) +0.10d = 2.10 . . . . substitute for 27-d for n

1.35 +0.05d = 2.10 . . . . . . . . . simplify

0.05d = 0.75 . . . . . . . . . . . . . . subtract 1.35

d = 15 . . . . . . . . . . . . . . . . . . . . divide by 0.05

n = 27 -d = 12

Alexandra has 12 nickels and 15 dimes.

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Alternate solution (using elimination)

For the system of equations above, you can divide the first equation by .05 and get ...

n + 2d = 42

Now, you can subtract the second equation, eliminating the n variable:

(n +2d) -(n +d) = (42) -(27)

d = 15 . . . . . simplify