Sandra has 8 coins that equal 87 cents what coins does she have
She has to have 2 pennies. The remaining 6 = 85 cents. 2 quarters, 3 dimes and a nickel = 6 coins = 85 cents.
Yes that's the correct answer
that is correct
To determine the types of coins that Sandra has, we can use a system of equations based on the given information.
Let's assume that Sandra has x quarters, y dimes, and z pennies.
Since Sandra has a total of 8 coins, we can express this mathematically as:
x + y + z = 8 (Equation 1)
In addition, the total value of these coins is 87 cents. We know that 1 quarter is worth 25 cents, 1 dime is worth 10 cents, and 1 penny is worth 1 cent. Therefore, the value equation can be written as:
25x + 10y + z = 87 (Equation 2)
Now we have a system of two equations with three variables. To solve this system, we'll take a specific approach.
1. Solve Equation 1 for z:
z = 8 - x - y
2. Substitute the value of z in Equation 2:
25x + 10y + (8 - x - y) = 87
3. Simplify the equation:
24x + 9y = 79 (Equation 3)
The system of equations now becomes:
x + y + z = 8 (Equation 1)
24x + 9y = 79 (Equation 3)
To solve this system, we can use various methods, such as substitution, elimination, or graphing. Let's solve it using the elimination method:
Multiply Equation 1 by 9 to eliminate y:
9x + 9y + 9z = 72 (Equation 1 multiplied by 9)
Subtract Equation 3 from the modified Equation 1:
9x + 9y + 9z - 24x - 9y = 72 - 79
-15x + 9z = -7
Now, rearrange the equation:
15x - 9z = 7 (Equation 4)
We have two equations for two variables:
24x + 9y = 79 (Equation 3)
15x - 9z = 7 (Equation 4)
Solving these equations simultaneously will give us the values of x, y, and z.
After solving the system of equations, if the solution exists, you will find the values for x, y, and z. These values will represent the number of quarters, dimes, and pennies that Sandra has, respectively.