Question

A vending​ machine's coin box contains​ nickels, dimes, and quarters. The total number of coins in the box is 252 . The number of dimes is three times the number of nickels and quarters together. If the box contains dollars 24 and ​cents 85, find the number of​ nickels, dimes and quarters that it contains.

here are ​nickels,
​dimes,
quarters in the coin box.

Answer 1

Step-by-step explanation :

N = number of nickels

D = number of dimes

Q = number of quarters

`

252 = N + D + Q <---- Equation 1

D = 3(N+Q) <---- Equation 2

24.85 = 0.05N + 0.10D + 0.25Q <---- Equation 3

We a have set of three linear equations to solve for three unknowns N, D, and Q.

Rearranging the equations we have :

N + D + Q = 252

3N - D + 3Q = 0

0.05N + 0.10 D + 0.25Q = 24.85

Solving the set of linear equations, we end up with :

N = 49

D = 189

Q = 14

(see the attached images for the entire solution)