The sum of three whole numbers is 193. The smaller two are consecutive integers and the larger two are consecutive even whole numbers.Find the three whole numbers.
Let the smallest number be x.
x + (x+1) + (x+3) = 193
3x + 4 = 193
3x = 189
x = 63
So the numbers are 63, 64 and 66.
If you are not allowed to use algebra (as I just did), you will have to try numbers just above 60 until you find a group that works.
Let's solve this step by step.
Let's assume the smaller consecutive integers are n and n+1.
And let's assume the larger consecutive even numbers are m and m+2.
According to the given information,
n + (n+1) + m + (m+2) = 193
Combining like terms,
2n + 2m + 3 = 193
Simplifying,
2n + 2m = 190
Dividing both sides by 2,
n + m = 95
Since n and m are consecutive integers, their sum will always be odd.
But 95 is an odd number, it means either n or m is not an integer.
Therefore, there is no solution for this problem.
To find the three whole numbers, let's break down the problem into steps:
Step 1: Let's define the variables.
- Let's define the three whole numbers as a, b, and c.
Step 2: Translate the given information into equations.
- The sum of the three whole numbers is 193, so we can write the equation as: a + b + c = 193.
- The smaller two numbers are consecutive integers, so we can write the equation as: b = a + 1.
- The larger two numbers are consecutive even whole numbers, so we can write the equation as: c = b + 2.
Step 3: Substitute the equations into one another.
- Substitute b = a + 1 into the third equation to get: c = (a + 1) + 2, which simplifies to c = a + 3.
Step 4: Rewrite the first equation by substituting the values from the second and third equations.
- Replace b with a + 1 and c with a + 3 in the first equation: a + (a + 1) + (a + 3) = 193.
- Simplify the equation: 3a + 4 = 193.
- Subtract 4 from both sides of the equation: 3a = 189.
Step 5: Solve for a.
- Divide both sides of the equation by 3: a = 63.
Step 6: Find b and c.
- Substitute the value of a into the second and third equations.
- Substitute a = 63 into the equation b = a + 1 to get b = 63 + 1, which simplifies to b = 64.
- Substitute a = 63 into the equation c = a + 3 to get c = 63 + 3, which simplifies to c = 66.
Therefore, the three whole numbers are 63, 64, and 66.