Laverne has sixty-one coins, all of which are dimes and quarters. If the totoal value is $9.85, how many of each kind of coin she has?

Let's solve this problem step by step.

Step 1: Let's assume Laverne has x dimes and y quarters.

Step 2: We know that the total number of coins is 61. So we have the equation:

x + y = 61 (Equation 1)

Step 3: We also know that the total value of the coins is $9.85. The value of a dime is $0.10 and the value of a quarter is $0.25. So we can write another equation for the total value:

0.10x + 0.25y = 9.85 (Equation 2)

Step 4: Now we need to solve these two equations simultaneously.

Multiplying Equation 1 by 0.10, we get:

0.10x + 0.10y = 6.10 (Equation 3)

Subtracting Equation 3 from Equation 2, we eliminate the term with x:

0.10x + 0.25y - (0.10x + 0.10y) = 9.85 - 6.10

0.10x - 0.10x + 0.25y - 0.10y = 3.75

0.15y = 3.75

Step 5: Divide both sides of the equation by 0.15:

y = 3.75 / 0.15

y = 25

Step 6: Substitute the value of y back into Equation 1 to find x:

x + 25 = 61

x = 61 - 25

x = 36

Step 7: Laverne has 36 dimes and 25 quarters.

Therefore, Laverne has 36 dimes and 25 quarters.

To solve this problem, we can set up a system of equations. Let's assume Laverne has x number of dimes and y number of quarters.

The first equation represents the total number of coins:
x + y = 61

The second equation represents the total value of the coins:
0.10x + 0.25y = 9.85

Now we can solve this system of equations to find the values of x and y.

One way to solve this is by substitution. We can solve the first equation for x and substitute it into the second equation. Let's solve the first equation for x:

x = 61 - y

Now we substitute this value of x into the second equation:

0.10(61 - y) + 0.25y = 9.85

Simplifying the equation:

6.1 - 0.10y + 0.25y = 9.85

Combining like terms:

0.15y = 3.75

Dividing both sides by 0.15:

y = 3.75 / 0.15 = 25

Now we substitute this value of y back into the first equation to solve for x:

x + 25 = 61
x = 61 - 25 = 36

Therefore, Laverne has 36 dimes and 25 quarters.

Let D be the number of dimes and Q be the number of quarters. Use algebra.

D + Q = 61
10 D + 25 Q = 985

Solve that pair of equations.

10 D + 25 (61 -D) = 985
15 D = 540
D = 36
Q = 61 - 36 = 25