Question

There are two more quarters than dimes, and as many nickels, as quarters and dimes together. the total amount of money is $3.75. how many quarters, dimes, and nickels are there?

Answer 1

9 quarters, 7 dimes, and 16 nickels.

Answer 2

Answer:

There are 7 dimes, 9 quarters and 16 nickels.

Step-by-step explanation:

Let's start by defining the variables for this problem :

Q : ''number of quarters''

D : ''number of dimes''

N : ''number of nickels''

''There are two more quarters than dimes'' so we can write the following equation :

$Q=D+2$

''And as many nickels, as quarters and dimes together'' so we can write the following equation :

$N=Q+D$

''The total amount of money is $3.75'' so we can write the following equation :

$0.25Q+0.10D+0.05N=3.75$

We must solve the following system :

$Q=D+2$ (I)

$N=Q+D$ (II)

$0.25Q+0.10D+0.05N=3.75$ (III)

In the equation (II) we can find Q in terms of N and D :

$N=Q+D$

$Q=N-D$ (IV)

If we use (I) in (IV) :

$Q=N-D$

$D+2=N-D$

$2D=N-2$

$N=2D+2$ (V)

If we use (I) and (V) in (III)

$0.25Q+0.10D+0.05N=3.75$

$(0.25).(D+2)+0.10D+(0.05).(2D+2)=3.75$

$0.25D+0.50+0.10D+0.1D+0.1=3.75$

$0.45D=3.15$

$D=\frac{3.15}{0.45}=7$

$D=7$

If $D=7$ ⇒ replacing in (I)

$Q=D+2$

$Q=7+2=9$

$Q=9$

If we replace this values in (II) ⇒

$N=Q+D$

$N=9+7=16$

$N=16$

We find that there are 7 dimes, 9 quarters and 16 nickels