dara has 5 coins in her purse the coins total 40 cents
3 dimes, 2 nickels
To solve this question, we need to determine the values of the coins that Dara has in her purse.
Let's assume that Dara has x number of pennies (1 cent coins), y number of nickels (5 cent coins), and z number of dimes (10 cent coins).
Given that Dara has a total of 5 coins, we can set up an equation:
x + y + z = 5 (equation 1)
We are also given that the total value of the coins is 40 cents. Since pennies are worth 1 cent, nickels are worth 5 cents, and dimes are worth 10 cents, we can write another equation:
x + 5y + 10z = 40 (equation 2)
Now, we have a system of equations that we can solve simultaneously.
To solve the system, we can use substitution or elimination. Let's use elimination to solve it:
Multiply equation 1 by -5 to make the y terms cancel out:
-5x - 5y - 5z = -25 (equation 3)
Add equation 2 and equation 3 together:
x - 4z = 15
We can then substitute this value for x into equation 1:
(15 - 5y) + y + z = 5
15 - 4y + z = 5
-4y + z = -10
Now, we have two equations that we can solve:
x - 4z = 15 (equation 4)
-4y + z = -10 (equation 5)
Let's solve equation 5 for z:
z = -10 + 4y
Substitute this value for z into equation 4:
x - 4(-10 + 4y) = 15
x + 40 - 16y = 15
x - 16y = -25 (equation 6)
Now we have two equations:
x - 16y = -25 (equation 6)
-4y + z = -10 (equation 5)
From equation 5, we can express z in terms of y:
z = -10 + 4y
Substitute this value for z in equation 6:
x - 16y = -25
Rearranging equation 6 gives us:
x = 16y - 25
To find the possible values for x and y, we can try different values for y and calculate the corresponding values of x.
For example, let's try y = 1:
x = 16(1) - 25
x = 16 - 25
x = -9
So, if y = 1, then x = -9. But since we can't have a negative number of coins, this combination is not possible.
Let's try y = 2:
x = 16(2) - 25
x = 32 - 25
x = 7
If y = 2, then x = 7. This is a valid combination.
Therefore, Dara has 7 pennies (x = 7), 2 nickels (y = 2), and -10 + 4(2) = -10 + 8 = -2 dimes (z = -2) in her purse. However, since we can't have a negative number of dimes, this combination is also not possible.
Based on the given information, there seems to be an error or inconsistency. If you have any other details or clarification, I'll be happy to assist you further.