Question

I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $20. Then it occurred to me that, if my nickels were dimes and my dimes were quarters, I would have $46.25. How many dimes and nickels are in the box?

Answer 1

It depends. There could be ten dimes and twenty nickels or one dime and thirty-nine nickels. Maybe word this differently.

Answer 2

There are 150 nickels and 125 dimes in the box.

Let x = the number of nickels in the box

Let y = the number of dimes in the box

Firstly, we have to convert value of nickels and dimes into cents.

Value of 1 nickel = 5 cents

Value of 1 dime = 10 cents

Value of 1 dollar = 100 cents

Thus, the equation (1) (in cents) can be written as:

x + 2y = 400 Equation (1)

If my nickels were dimes and dimes were quarters:

A quarter is worth 25 cents.

Thus, the equation (2) (in cents) can be written as:

5x+10y =2000

5(x+2y)= 2000

x+2y = 2000/5

2x + 5y = 925 Equation (2)

Multiply Equation (1) by "2", we get:

10x +25y= 4625

5(2x+5y)=4625

2x+5y=4625/5

2x + 4y = 800 Equation (1)

Subtraction Equation (1) from Equation (2):

2x +5y-2x -4y=925-800

y= 125

2x + 5y = 925

2x + 5 × 125 = 925

2x + 625 = 925

2x = 925 - 625

2x = 300

x = 150

There are 150 nickels and 125 dimes in the box.

Here, we can check it by putting the value of x and y in Equation (1):

5x + 10y = 2000

5× 150 + 10 × 125 = 2000

750 + 1250 = 2000

2000 = 2000

There are 150 nickels and 125 dimes in the box.