Answer:
Step-by-step 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
