Question

Nolan has some nickels and some dimes. He has no more than 19 coins worth no less than $1.30 combined. If Nolan has 5 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values.

Answer 1

Explanation:

A nickel is worth 5 cents. Converting to dollars, it becomes

5/100 = $0.05

A dime is worth 10 cents. Converting to dollars, it becomes

10/100 = $0.1

Let x represent the number if nickels.

Let y represent the number of dimes.

He has no more than 19 coins. This means that

x + y ≤ 19

He has no less than $1.30 combined. This means that

0.05x + 0.1y ≥ 1.3

If Nolan has 5 nickels, then, substituting x = 5 into x + y ≤ 19, it becomes

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

substituting x = 5 into 0.05x + 0.1y ≥ 1.3, it becomes

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 1.05/0.1

y ≥ 10.5

Therefore, all possible values for the number of dimes that he could have would be

10.5 ≤ y ≤ 14