Find two mixed numbers so that the sum is 8 4/8 and the difference is 2 2/8
6 1/4 and1 1/4
To find two mixed numbers that satisfy the given conditions, we can set up a system of equations.
Let's assume the two mixed numbers are A and B.
According to the given conditions:
1) The sum of A and B is 8 4/8 or 8.5 when written as a decimal.
2) The difference between A and B is 2 2/8 or 2.25 when written as a decimal.
We can set up the following equations:
Equation 1: A + B = 8.5
Equation 2: A - B = 2.25
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using substitution:
1) Solve Equation 2 for A: A = 2.25 + B
2) Substitute A in Equation 1 with the value from Equation 2: 2.25 + B + B = 8.5
3) Simplify the equation: 2B = 8.5 - 2.25
2B = 6.25
4) Divide both sides of the equation by 2: B = 6.25 / 2
B = 3.125
Now, substitute the value of B back into Equation 2 to find A:
A = 2.25 + B
A = 2.25 + 3.125
A = 5.375
Therefore, the two mixed numbers that satisfy the given conditions are:
A = 5 3/8
B = 3 1/8
Let x = one number and y = the other.
x + y = 8 4/8
x - y = 2 2/8
Add the two equations.
2x = 10 6/8
x = 5 3/8
Insert x value into one of the equations to find y.