Let number of nickels be n
and number of dimes be d
we know that there are 4 more nickels than there are dimes
⇒ n = d + 4
We have to find out ratio of d and n
[tex]\frac{d}{n} = \frac{d}{d+4}[/tex]
Now, let's substitute the values of each of the option to see whether the values we obtain for d and n are positive or not
(A) 8/10
⇒ \frac{d}{d+4}[/tex] = 8 / 10
⇒ 10 × d = 8 × d + 32
⇒ 2 × d = 32
⇒ d = 16
Hence, n = d+4 = 20. Since n and d are positive values. A is the correct answer
Nevertheless, let's take a look at the other options as well
(B) 1
⇒ \frac{d}{d+4}[/tex] = 1
⇒ d = d + 4
This equation can't be solved since we would be left with 0=4, which doesn't hold true, So B is not the correct answer
(C) 14/10
⇒ \frac{d}{d+4}[/tex] = 14 / 10
⇒ 10 × d = 14 × d + 56
⇒ -4 × d = 56
⇒ d = -16
Since d is negative, it can't represent the number of dimes. So C is not the correct answer.
(D) 4
⇒ \frac{d}{d+4}[/tex] = 4
⇒ d = 4 × d + 16
⇒ d = (-16/3)
Since d is negative, it can't represent the number of dimes. So D is not the correct answer.
(E) None of the above
This is not the correct answer as we have already seen that A is the correct answer.
