Question

A drawer contains quarters and nickels. There are 200 total coins valuing $30.00. Think about a system of equations that can be used to represent the number of quarters and nickels, and then think through using substitution to solve the system of equations.
How many nickels are in the jar?

110


90


100


120

Answer 1

Answer:

100

Step-by-step explanation:

Let n and q represent the numbers of nickels and quarters, respectively. A suitable system of equations is ...

  n + q = 200 . . . . . . there are 200 coins in the drawer

  5n +25q = 3000 . . .their value is $30.00

For mixture problems like this, it is often a good idea to substitute for the variable representing the contributor of lower value. That is, we want to write an expression for n that we can use for substitution.

Using the first equation to solve for n, ...

  n = 200 - q

Substituting this into the second equation gives ...

  5(200 -q) +25q = 3000

  1000 +20q = 3000 . . . . . . simplify

  20q = 2000 . . . . . . . . . . . . subtract 1000

  q = 100 . . . . . . . . . . . . . . . . divide by 20

  n = 200 -q = 100 . . . . . . . . the number of nickels, as we want

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Comment on the solution

We solved for q, then had to do an extra step to find the value of n that the problem asks for. Had we written q = 200-n and used that for substitution, we would have ended with the equation -20n = -2000. This would give the answer for n directly (with no additional steps required).

Sometimes working with negative numbers is uncomfortable or results in errors, so we chose to use the solution method that would avoid negative numbers.

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Comment on the problem statement

We are told about coins in a drawer, and we are asked about coins in a jar. There is not enough information to answer the question asked. We have had to assume that both refer to the same quantity of coins—an assumption that is not supported by anything in the problem statement.

Answer 2

Answer:

100

Step-by-step explanation:

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