Question

A coin bank contains 25 coins in nickels, dimes, and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank?

Answer 1

15 nickels

8 dimes

2 quarters

Explanation:

Let n= number of nickles

Let d = number of dimes

Let q + number of quarters

n + d + q + 25

d = 4q

.05n + .10d + .25q = 2.05

I am going to take the last equation and multiply it though by 100 to clear the decimal to get

5n + 10d + 25q = 205

Substitute in 4q for d for the first and third equations

n + 4q + q = 25

n + 5q = 25

5n + 10d + 25q = 205

5n + 10(4q) + 25q = 205

5n + 40q + 25q = 205

5n + 65q = 205

Multiply n + 5q = 25 all the way through by -5 and add it to 5n + 65Q = 205

n + 5q = 25

-5(n) + -5(5q) = -5(25)

-5n -25q + -125

5n + 65q = 205

40q = 80 Divide both sides by 40

q = 2 There are 2 quarters.

Substitute 2 for q in

d = 4q

d = 4(2)

d = 8 There are 8 dimes.

Substitute q = 2 and d =8 to find n

n + d + q = 25

n + 8 + 2 = 25

n + 10 = 25 Subtract 10 from both sides

n = 15 There are 15 nickels.

Answer 2

Dimes = A
Quarters = B
There are four times Dimes as that of quarters in a bank of 25 coins which can be put into:
Dimes = A = 4B
We know that
A+B=25 Substitute value of A=4B to get
4B + B = 25
5B = 25
B = 25/5 = 5
Therefore Dimes = A = 4B = 4*5 = 20 and Quarters = B = 5
Answer: number of Dimes in a coin bank = A = 20