1. the sum of 3 numbers is 207. the 2nd # is 8 times the first, while the third is 3 less than the first. find the #s.
2. the sumof 3 numbers is 161. the second number is 6 times the first, and the third is 5 more than the second. find the #s.
Thanks so much!
problem 1.
let x = first number
8x = second number
x - 3 = third number
x + (8x) + (x-3) = 207
simply the equation and solve for x
problem 2 is done the same way as the first one
You're welcome! I would be happy to help you solve these problems.
Let's start with the first problem:
1. The sum of 3 numbers is 207. The second number is 8 times the first, while the third is 3 less than the first. Find the numbers.
To solve this problem, we can use algebraic equations. We can represent the first number as 'x', the second number as '8x', and the third number as 'x - 3' based on the given conditions.
According to the problem, the sum of the three numbers is 207. So we can write the equation:
x + 8x + (x - 3) = 207.
Combining like terms, we have:
10x - 3 = 207.
Adding 3 to both sides of the equation, we get:
10x = 210.
Dividing both sides of the equation by 10, we find:
x = 21.
Now we have the value of the first number, which is 21, and we can substitute it back into the expressions for the second and third numbers:
Second number = 8x = 8 * 21 = 168.
Third number = x - 3 = 21 - 3 = 18.
Therefore, the three numbers are 21, 168, and 18.
Let's move on to the second problem:
2. The sum of 3 numbers is 161. The second number is 6 times the first, and the third is 5 more than the second. Find the numbers.
Similar to the previous problem, we will assign variables to the numbers: the first number as 'x', the second number as '6x', and the third number as '6x + 5'.
The sum of the three numbers is 161, so we can write the equation:
x + 6x + (6x + 5) = 161.
Combining like terms, we have:
13x + 5 = 161.
Subtracting 5 from both sides of the equation, we get:
13x = 156.
Dividing both sides of the equation by 13, we find:
x = 12.
Now we have the value of the first number, which is 12, and we can substitute it back into the expressions for the second and third numbers:
Second number = 6x = 6 * 12 = 72.
Third number = 6x + 5 = 6 * 12 + 5 = 77.
Therefore, the three numbers are 12, 72, and 77.
I hope this explanation helps you understand how to solve these types of problems! If you have any more questions, feel free to ask.