find two mixed numbers so that the sum is 16 and the difference is 15.
find three mixed numbers so that the least number is 5 1/5.
x + y = 16
x - y = 15
add the two equations
2x = 31 so x= 31/2 or 15 1/2
So then y = 1/2
so why is y= 1/2?
To find two mixed numbers whose sum is 16 and difference is 15, let's break it down step by step:
Step 1: Assign variables:
Let's assign the first mixed number as x and the second mixed number as y.
Step 2: Write equations:
According to the given information, the sum of the two mixed numbers is 16, so we can write the equation: x + y = 16.
Also, the difference between the two mixed numbers is 15, so we can write the equation: x - y = 15.
Step 3: Solve the system of equations:
To solve the system of equations, we can use the method of substitution or elimination.
Using substitution:
From the first equation, we can rewrite it as x = 16 - y.
Substituting this value of x into the second equation, we get (16 - y) - y = 15.
Simplifying, we have 16 - 2y = 15.
Rearranging, we get -2y = -1.
Dividing both sides by -2, we find y = 1/2.
Substituting this value of y back into the first equation, we have x + (1/2) = 16.
Subtracting 1/2 from both sides, we find x = 31/2.
So, the two mixed numbers that satisfy the conditions are x = 31/2 and y = 1/2.
To find three mixed numbers where the least number is 5 1/5, let's follow these steps:
Step 1: Assign variables:
Let's assign the first mixed number as x, the second mixed number as y, and the third mixed number as z.
Step 2: Write conditions:
According to the given information, the least number is 5 1/5, which can be written as 26/5.
Step 3: Set up inequalities:
To ensure that the least number is 5 1/5, we can set up the inequalities:
x ≥ 26/5
y ≥ x
z ≥ y
Step 4: Choose values:
We can choose any values that satisfy the given conditions. One possible set of values could be:
x = 26/5
y = 27/5
z = 28/5
These values satisfy the conditions where the least number is 5 1/5 and y is greater than or equal to x, and z is greater than or equal to y.
Please note that there are multiple correct answers for the three mixed numbers, and the values can be different as long as they meet the given conditions.