What are three numbers that have a sum of 35 if the greatest number is 14 more than the least number?
let smallest number be x
let the largest number be x+14
let the middle number be y , such that y > x
x + x+14 + y = 35
2x + y = 21
y = -2x + 21
There is an infinite number of such triplets
e.g.
5, 11, 19
4, 13, 18
6, 9, 20
4.532, 11.936 , 18.532
1, 19, 15 ---> reject that one, since it does not satisfy both conditions.
... etc
There are infinitely many answers.
Even restricting yourself to integers, you have:
2, 16, 17 or 5, 19, 11 or 18, 32, -15.
Well, let's use the power of humor to solve this mathematical riddle! We have three numbers with a sum of 35 and the greatest number being 14 more than the least number. So, we can call the least number "X," and the greatest number will be "X + 14." Now, let's add a pinch of arithmetic humor!
We have X + X + (X + 14) = 35.
That simplifies to 3X + 14 = 35.
Now, subtract 14 from both sides to make the equation less "negative"!
3X = 21.
And with one last bit of mathematical humor, we divide both sides by 3 to find X.
X = 7.
So, the three numbers that meet the criteria are X = 7, X + 14 = 7 + 14 = 21, and X + X + (X + 14) = 7 + 7 + 21 = 35!
Let's call the least number x. According to the given information, the greatest number is 14 more than the least number. So, the greatest number would be x + 14.
Now we know the sum of the three numbers is 35. Therefore, we can write the equation:
x + (x + 14) + ? = 35
Since we are only asked for three numbers, we need to determine the value of the missing number from the equation.
To find the missing number, we will substitute the given information into the equation and solve for x:
x + (x + 14) + ? = 35
2x + 14 + ? = 35
2x + ? = 21
At this point, we don't have enough information to solve for x or the missing number. The given information is not sufficient to determine all three numbers.
To find three numbers that have a sum of 35, we need to set up a system of equations. Let's assume the three numbers are x, y, and z.
From the given information, we know that the greatest number (z) is 14 more than the least number (x). We can express this as:
z = x + 14 --------------- Equation 1
We also know that the sum of the three numbers (x + y + z) is 35. Therefore, we can write:
x + y + z = 35 -------------- Equation 2
Now, we have a system of two equations with two unknowns (x and z). We can solve this system to find the values of x, y, and z.
First, substitute the value of z from Equation 1 into Equation 2:
x + y + (x + 14) = 35
Simplify:
2x + y + 14 = 35
Rearrange the equation:
2x + y = 21 -------------- Equation 3
Now we have a system of two equations: Equation 1 (z = x + 14) and Equation 3 (2x + y = 21).
From here, we have multiple ways to solve the system. Let's use the method of substitution:
1. Solve Equation 1 for z:
z = x + 14
2. Substitute z in Equation 3 with the expression x + 14:
2x + y = 21
x + 14 + y = 21
3. Simplify:
2x + y = 21
x + y = 7 -------------- Equation 4
Now we have a system of two linear equations:
x + y = 7
2x + y = 21
We can solve this system using any method such as substitution or elimination.
Let's use the method of elimination:
- Multiply Equation 4 by -1 to make the coefficients of y equal:
-1(x + y) = -1(7)
-x - y = -7
-2x - 2y = -14
-2x - y = - 21
-2x - y = -21
Add the two equations:
-2x - y + 2x + y = -14 + (-21)
0 = -35
The resulting equation is inconsistent, meaning there is no solution. Therefore, there are no three numbers that satisfy the given conditions.