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Dahasolnce [82]

3 years ago

11

A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is

$9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.

1 answer:

telo118 [61]3 years ago

7 0

Answer:

There are 65 dimes. There are 55 nickels.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of dimes

y is the number of nickels.

There are a total of 120 coins in the bag

This means that x + y = 120.

The total value of the coins is $9.25.

The dime is worth $0.10 and the nickel is worth $0.05. So

0.1x + 0.05y = 9.25

System:

$x + y = 120$

$0.1x + 0.05y = 9.25$

From the first equation:

$y = 120 - x$

Replacing in the second:

$0.1x + 0.05y = 9.25$

$0.1x + 0.05(120 - x) = 9.25$

$0.1x + 6 - 0.05x = 9.25$

$0.05x = 3.25$

$x = \frac{3.25}{0.05}$

$x = 65$

$y = 120 - x = 120 - 65 = 55$

There are 65 dimes. There are 55 nickels.

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Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

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