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How many of each type of coin is in the bag?

How many of each type of coin is in the bag?-example-1

1 Answer

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18 votes

Answer:

Number of pennies: 125

Number of nickels: 95

Number of dimes: 95

Step-by-step explanation:

Let's call x the number of pennies, y the number of nickels, and z the number of dimes.

If the child has 315 coins, we get:

x + y + z = 315

Additionally, they worth $15.50, so

0.01x + 0.05y + 0.10z = 15.50

Because a penny has a value of $0.01, a nickel has a value of $0.05 and a dime has a value of $0.10

Finally, the bag contains the same number of nickels and dimes, so

z = y

Therefore, we have the following system of equation:

x + y + z = 315

0.01x + 0.05y + 0.10z = 15.50

z = y

Replacing the last equation on the first one, we get:

x + y + z = 315

x + y + y = 315

x + 2y = 315

Then, we can solve the equation for x, so

x + 2y - 2y = 315 - 2y

x = 315 - 2y

Now, we need to replace z = y and x = 315 - 2y on the second equation of the system

0.01x + 0.05y + 0.10z = 15.50

0.01(315 - 2y) + 0.05y + 0.10y = 15.50

0.01(315) - 0.01(2y) + 0.05y + 0.10y = 15.50

3.15 - 0.02y + 0.05y + 0.10y = 15.50

3.15 + 0.13y = 15.50

And solve for y

3.15 + 0.13y - 3.15 = 15.50 - 3.15

0.13y = 12.35

0.13y/0.13 = 12.35/0.13

y = 95

With the value of y, we can find the value of x and z as follows

x = 315 - 2y

x = 315 - 2(95)

x = 315 - 190

x = 125

z = y

z = 95

Then, there are 125 pennies, 95 nickels, and 95 dimes

Therefore, the answers are

Number of pennies: 125

Number of nickels: 95

Number of dimes: 95

User Alexander Derck
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