Bag of Nickles and Quarters

Question

Maricella has a bag containing 35 nickles and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions? Im doing a math project and another part of it says I have to use the substitution method. Can you show me how to solve this problem with the substitution method?

Answer 1

So this time you want the answer using substitution method? Very well. Reposting the expressions!

n + q = 35

0.05n + 0.25q < 2.5

 

Since we want the inequality to focus on the quarters, let's isolate n in the equation. Subtract q from both sides:

n = 35 - q

Now input that into the inequality:

0.05(35 - q) + 0.25q < 2.5

Distribute:

1.75 - .05q + .25q < 2.5

Simplify:

1.75 + .2q < 2.5

Subtract 1.75:

.2q < .75

Divide by .2:

q < 3.75, leaving the maximum number of quarters to be 3.

 

As you can see, we came up with the exact same answer as the elimination method you requested earlier.