Question

a jar contains n nickels and d dimes. there are 20 coins in the jar, and the total value of the coins is $1.40. how many nickels and how many dimes are in the jar?

Answer 1

Answer : The number of nickel and dimes in the jar are, 12 and 8 respectively.

Step-by-step explanation :

As we are given that:

Number of nickels = n

Number of dimes = d

As, there are 20 coins in the jar. The equation will be:

`n+d=20` .........(1)

or,

`d=20-n` ............(2)

Total value of the coins is $1.40. The equation will be:

As we know that:

1 dime = $ 0.1

1 nickel = $ 0.05

So,

`0.05n+0.1d=1.40` ........(3)

Now put equation 2 in equation 3, we get:

`0.05n+0.1* (20-n)=1.40`

`0.05n+2-0.1n=1.40`

`0.05n+2-0.1n=1.40`

`2-0.05n=1.40`

`0.05n=2-1.40`

`0.05n=0.6`

`n=(0.6)/(0.05)`

`n=12`

Now put the value of 'n' in equation 2, we get:

`d=20-n`

`d=20-12`

`d=8`

Thus, the number of nickel and dimes in the jar are, 12 and 8 respectively.

Answer 2

12 nickels and 10 dimes
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0.05n + 0.10d = 1.40
n + d = 20
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substitution-

n+d = 20 changes to d = 20 - n
0.05n + 0.10(20-n) = 1.40
0.05n + 2 - 0.10n = 1.40
-0.05n -2 -2

-0.05n = -0.60

n = 12

Replace n with 12 and solve for d
---------------------------------

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12 + d = 20
d = 8