A box contains 76 coins, only dimes and nickels. The amount in the box is $4.90. How many dimes and how many nickels are in the box?

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.

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