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. If there are no possible solutions, submit an empty answer.

Answer 1

number of dimes 11 to 14

Explanation:

given data

coin = 19

worth no less = $1.30

Nolan nickles = 5

solution

we convert 5 cent to dollars, it will be

5÷100 = $0.05

and

dime is worth 10 cents

so it will be 10 ÷ 100 = $0.1

so we consider here x as the number when nickels.

and we consider y as the number of dimes.

so here we can say

x + y ≤ 19 ..........................1

as here no less than $1.30 combined.

so

0.05 x + 0.1 y ≥ 1.3 ......................2

and

when Nolan has 5 nickels

put x = 5 in eq 1

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

and

now we put x = 5 in eq 2

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 10.5

so all possible values for the number of dimes 11 to 14