Which two dates have a quotient of 3 and a sum of 32.
Dates are 1-30...
24 and 8
To find two dates that have a quotient of 3 and a sum of 32, we can use algebra. Let's denote the first date as x and the second date as y.
According to the given conditions, we have two equations:
1. x * y = 3
2. x + y = 32
We can solve these equations simultaneously to find the values of x and y.
From equation 2, we can express y in terms of x:
y = 32 - x
Substituting this value of y into equation 1:
x * (32 - x) = 3
Expanding the equation:
32x - x^2 = 3
Rearrange the equation:
x^2 - 32x + 3 = 0
Now we can solve this equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
In this case, a = 1, b = -32, and c = 3. Substituting these values:
x = (32 ± √((-32)^2 - 4*1*3))/2*1
Simplifying:
x = (32 ± √(1024 - 12))/2
x = (32 ± √1012)/2
Calculating the square root of 1012:
x ≈ (32 ± 31.83)/2
Now, let's find the possible values for x:
1. x = (32 + 31.83)/2 ≈ 31.91
2. x = (32 - 31.83)/2 ≈ 0.08
Since the dates range from 1 to 30, the value of x should fall within this range. Therefore, the date is approximately 31.91, which is not possible in this case.
Hence, there are no two dates between 1 and 30 with a quotient of 3 and a sum of 32.
To find the two dates with a quotient of 3 and a sum of 32, we will set up a system of equations.
Let's say the first date is x and the second date is y.
Given:
x + y = 32 (The sum of the two dates is 32)
x / y = 3 (The quotient of the two dates is 3)
Now we can solve this system of equations to find the values of x and y.
From the first equation, we can isolate x:
x = 32 - y
Now we can substitute this value of x in the second equation:
(32 - y) / y = 3
Simplify the equation by multiplying both sides by y:
32 - y = 3y
Add y to both sides:
32 = 4y
Divide both sides by 4:
y = 32/4
y = 8
Now substitute this value of y back into the first equation to find x:
x + 8 = 32
x = 32 - 8
x = 24
Therefore, the two dates that have a quotient of 3 and a sum of 32 are 24 and 8.