Suzie has 11 coins in her purse. the coins are dimes and quarters. If she has $2.00 in her purse, how many of each coin does she have?
10 d + 25(11-d) = 200
To find out how many dimes and quarters Suzie has, we can use a system of equations.
Let's say Suzie has "x" dimes and "y" quarters.
We know that the total number of coins she has is 11, so we can write the equation:
x + y = 11 -- Equation 1
We also know that the total value of the coins she has is $2.00, which can be expressed in cents as 200 cents. Since a dime is worth 10 cents and a quarter is worth 25 cents, the equation for the total value is:
10x + 25y = 200 -- Equation 2
Now we have a system of equations:
x + y = 11 -- Equation 1
10x + 25y = 200 -- Equation 2
We can solve this system of equations using various methods, such as substitution or elimination.
Let's use the substitution method. We can solve Equation 1 for x and substitute the expression into Equation 2:
x = 11 - y
10(11 - y) + 25y = 200
Now, we can simplify the equation and solve for y:
110 - 10y + 25y = 200
15y = 90
y = 6
Now that we have found the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 6 = 11
x = 11 - 6
x = 5
Therefore, Suzie has 5 dimes and 6 quarters.