Question

A collection of nickels and dimes is worth $6.10. There are 67 coins in all. How many nickels are there? 12 18 49 55

Answer 1

.05n + .10d = 6.10
n + d = 67
n = 67-d

.05(67-d) + .10d = 6.10
3.35 -.05d + .10d = 6.10
3.35 + .05d = 6.10
3.35-3.35 +.05d = 6.10-3.35
0.05d = 2.75
0.05d/0.05 = 2.75/0.05
d = 55

n + d = 67
n + 55 = 67
n = 12
There are 12 nickels

Check
0.5(12) + .10(55) = $6.10
.60 + 5.50 =$6.10
$6.10 = $6.10

Answer 2

A. 12

Explanation:

Let d represent the number of dimes and n represent the number of nickel.

We have been given that a collection of coins has 67 coins in all. This means that total number of nickels and dimes is 67. We can represent this information in an equation as:

`n+d=67...(1)`

Since we know that a dime is worth $0.10, so d dimes will be worth 0.10d. A nickel is worth $0.05, so n nickels will be worth 0.05n.

We are also told that the collection is worth $6.10. We can represent this information in an equation as:

`0.05n+0.10d=6.10...(2)`

We will use substitution method to solve system of linear equations.

From equation (1) we will get,

`d=67-n`

Upon substituting
`d=67-n` in equation (2) we will get,

`0.05n+0.10(67-n)=6.10`

`0.05n+6.70-0.10n=6.10`

`-0.05n+6.70=6.10`

`-0.05n+6.70-6.70=6.10-6.70`

`-0.05n=-0.60`

Let us divide both sides of our equation by
`-0.05`.

`(-0.05n)/(-0.05)=(-0.60)/(-0.05)`

`n=12`

Therefore, there are 12 nickels in the collection and option A is the correct choice.