The number of dimes is 75 coins.
The number of nickels is 1 coin.
Step-by-step explanation:
It is given that,
A box contains 76 coins, only dimes and nickels.
This is represented by the system of equations :
x + y = 76 -------(1)
10x + 5y = 4.90 ------(2)
Multiply eq (1) by 5 and subtract eq (2) from eq (1),
5x + 5y = 380
-(10x + 5y = 4.90)
-5x = 375.1
x = 375/5
x = 75 coins.
The number of dimes is 75 coins.
Substitute x=75 in eq (1),
y = 76 - 75
y = 1 coin.
The number of nickels is 1 coin.
The number of dimes present in the box is 22 and the number of nickel present is 54.
Explanation:
Given:
Number of coins = 76
Amount in the box = $4.9
Amount of nickel and dimes present = ?
Let d represent the number of dimes
n represent the number of nickels
d + n = 76 - 1
0.1d + 0.05n = 4.9 - 2
Multiply equation 1 with 0.1. It becomes
0.1d + 0.1n = 7.6 - 3
Solving equation 2 and 3
0.1d + 0.1n = 7.6
0.1d + 0.05n = 4.9
_______________________
0.05n = 2.7
n = 54
d + n = 76
d + 54 = 76
d = 22
Therefore, number of dimes present in the box is 22 and the number of nickel present is 54.
