Verified Answer :
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 : 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.