Question

A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00. If the collection contains 25 quarters, how many nickels can be in the collection? Let x = the number of quarters. Let y = the number of nickels.

Answer 1

The collection contains 25 quarters, and the number of nickels, represented as y, must satisfy the inequalities y ≥ 17 and y ≤ 35, resulting in 18 possible amounts of nickels.

Step-by-step explanation:

The question involves finding the possible number of nickels in a collection of coins consisting of quarters and nickels. Given that the collection has at least 42 coins and the total value does not exceed $8.00, we can set up inequalities to solve for the maximum number of nickels.

Let x be the number of quarters and y be the number of nickels. We are given that there are 25 quarters in the collection, so x = 25. Each quarter is worth 25 cents and each nickel is worth 5 cents. The total number of coins is at least 42, and the total value is at most $8.00, which translates to 800 cents.

Therefore, the inequalities we can set up are:

x + y ≥ 42

25x + 5y ≤ 800

Substituting x = 25 into the inequalities:

25 + y ≥ 42 (y ≥ 17)

25(25) + 5y ≤ 800 (625 + 5y ≤ 800, 5y ≤ 175, y ≤ 35)

So the number of nickels, y, can range from 17 to 35. This means there can be 18 different amounts of nickels in the collection.