Question

Sam runs a lemonade stand. One day he collected $6.55 in nickels and dimes. The number of nickels was 6 more than half the number of dimes. Find out how many dimes Sam collected.

Answer 1

Total number of dimes collected = 50

Explanation:

Let the number of dimes collected = d

And the number of nickels collected = n

On day collection in nickels and dimes = $6.55

Since, 1 nickel = $0.05

Therefore, 'n' nickels = 0.05n

And 1 dimes = $0.10

Value of 'd' dimes = $0.10d

Total value of 'n' nickels and 'd' dimes = $(0.05n + 0.10d)

So the equation for the total value will be,

0.05n + 0.10d = 6.55

5n + 10d = 655 --------(1)

Number of nickels was 6 more than half the number of dimes.

n =
`(d)/(2)` + 6 ------(2)

By substituting the value 'n' from equation (2) to equation (1)

5(
`(d)/(2)` + 6) + 10d = 655

`(5d)/(2)` + 30 + 10d = 655

`(25d)/(2)` = 655 - 30

25d = 625 × 2

d =
`(1250)/(25)`

d = 50

Therefore, total number of dimes collected = 50