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

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

Answer 2

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:

$0.05n+0.1\times (20-n)=1.40$

$0.05n+2-0.1n=1.40$

$0.05n+2-0.1n=1.40$

$2-0.05n=1.40$

$0.05n=2-1.40$

$0.05n=0.6$

$n=\frac{0.6}{0.05}$

$n=12$

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.