Find two mixed numbers so that the sum is 7 2/4 and the difference is 5
a+b=7 2/4
a-b=5
add the equations
2a=12 2/4
a=6 1/4
solve for b.
To find two mixed numbers that satisfy the given conditions, you can follow these steps:
Step 1: Write the given information as equations:
Let the two mixed numbers be represented by x and y.
The sum of the two mixed numbers is 7 2/4, which can also be written as 7 + 2/4 or 7.5.
The equation for the sum can be written as: x + y = 7.5
The difference of the two mixed numbers is 5.
The equation for the difference can be written as: x - y = 5
Step 2: Solve the system of equations:
Using the method of substitution or elimination, we can solve the system of equations.
Let's use the method of substitution:
From the equation x + y = 7.5, we can isolate x by subtracting y from both sides:
x = 7.5 - y
Substituting the value of x in the second equation, we get:
(7.5 - y) - y = 5
7.5 - 2y = 5
Next, isolate y by subtracting 7.5 from both sides:
-2y = 5 - 7.5
-2y = -2.5
Divide both sides by -2 to solve for y:
y = -2.5 / -2
y = 1.25
Now that we have the value of y, we can substitute it back into one of the original equations to find x:
From x + y = 7.5, we have:
x + 1.25 = 7.5
Subtract 1.25 from both sides:
x = 7.5 - 1.25
x = 6.25
Step 3: Check the answer:
Now that we have the values of x and y, let's check if they satisfy both equations:
For the sum: x + y = 7.5
6.25 + 1.25 = 7.5 (This is true)
For the difference: x - y = 5
6.25 - 1.25 = 5 (This is true)
Both equations are satisfied.
Step 4: Write the answer in mixed number form:
The two mixed numbers that satisfy the given conditions are 6 1/4 and 1 1/4.