Question

Hey vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin or in the machine.

Answer 1

vending machine has $ 41.25

Total conis t = 255

number of nickel coins = n

number of dime coins = d

number of quarter coins = q

total coins t = n + d + q = 255 -------> (1)

There are twice as many dimes as nickles

d = 2n ===> n = d/2 ------- > (2)

d = 2n substitute in (1) we get

n + 2n + q = 255

q = 255 - 3n --------> (3)

Total cost t = 41.25

(0.05)n + (0.10) d + (0.25) q = 41.25

(0.05) n + (0.10) 2n + ( 0.25) (255-3n) = 41.25

0.05n + 0.20 n + 63.75 - 0.75 n = 41.25

63.75 - 0.50 n = 41.25

0.50 n = 63.75 -41.25

0.50n = 22.5

n = 22.5 / 0.50

n= 45

from (2) ===> d = 2n = 2 × 45 = 90

from (3) ====> q = 255 - 3 × 45 = 255 - 135 = 120

n + d + q = 45 + 90 + 120 = 255

Nickles = 45

dimes = 90

Quarters = 120