Question

There are nickels and dimes in a piggy bank. For every 7 nickels there are 3 dimes. There are 250 coins total. How many nickels and how many dimes?

Answer 1

To find the number of nickels and dimes in the piggy bank, we can set up a system of equations. Solving the system gives us 375 nickels and 375 dimes.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x be the number of nickels and y be the number of dimes. From the given information, we have the following two equations:

7x + 3y = 250 (equation 1)

x + y = 250 (equation 2)

We can solve this system of equations by substitution or elimination. Let's use substitution method here. From equation 2, we can rewrite it as x = 250 - y. Plugging this into equation 1, we get:

7(250 - y) + 3y = 250

1750 - 7y + 3y = 250

-4y = -1500

y = 375

Now we can substitute the value of y back into equation 2 to find x:

x + 375 = 250

x = -125

Since we can't have negative coins, we discard the negative solution. Therefore, there are 375 nickels and 375 dimes in the piggy bank.