Jorge has a Total of 67 coins. All of which are dimes and nickels. The total value of the dimes and nickels i $5.40. Find the number of each type of coin.

There are 41 dimes and 26 nickels.

Step-by-step explanation:

From the information given, you know that you have 67 coins which would be:

x+y=67

Also, you now that the value of each coin is:

dimes= $0.10

nickels=$0.05

With this you can say that the number of dimes for its value plus the number of nickels for its value is equal to $5.40:

0.10x+0.05y=5.40

You will have the following equations:

x+y=67 (1)

0.10x+0.05y=5.40 (2), where:

x are the number of dimes

y are the number of nickels

First, you can solve for x in (1):

x=67-y

Then, you can replace (3) in (2):

0.10(67-y)+0.05y=5.40

6.7-0.10y+0.05y=5.40

1.3=0.05y

y=1.3/0.05

y=26

Now, you can replace the value of y in (3) to find x:

x=67-y

x=67-26

x=41

According to this, the answer is that there are 41 dimes and 26 nickels.

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