The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
what do they tell you?
x+y+z = 69
y = x-8
z = 5x
Now just substitute for y and z to find x, and then evaluate y and z.
1st no. = X.
2nd no. = x-8.
3rd no. = 5x.
x + (x-8) + 5x = 69.
X = 11.
x-8 =
5x =
Let's solve this step-by-step:
Let's assign variables to the three numbers:
- Let's call the first number "x".
- The second number is "x - 8".
- The third number is "5x".
According to the given information, the sum of the three numbers is 69.
So, we can set up the equation:
x + (x - 8) + 5x = 69
Now, let's solve the equation:
Combining like terms:
7x - 8 = 69
Adding 8 to both sides of the equation:
7x = 77
Dividing both sides of the equation by 7:
x = 11
Now, we can find the values of the second and third numbers:
- The second number: x - 8 = 11 - 8 = 3
- The third number: 5x = 5 * 11 = 55
Therefore, the three numbers are 11, 3, and 55.
To solve this problem, let's break it down step by step.
Let's assume the first number is "x."
According to the problem, the second number is equal to the first diminished by 8. So, the second number is (x - 8).
Also, the third number is 5 times the first number. Therefore, the third number is 5x.
Now, we are given that the sum of these three numbers is 69. So, we can write the equation:
x + (x - 8) + 5x = 69
Now, we can solve for x.
Combine like terms:
7x - 8 = 69
Add 8 to both sides:
7x = 77
Divide both sides by 7:
x = 11
Now, we have the value of the first number, which is 11.
To find the remaining two numbers, substitute the value of the first number back into the expressions we derived earlier.
The second number is (x - 8). So, the second number is (11 - 8) = 3.
The third number is 5 times the first number. So, the third number is 5 * 11 = 55.
Therefore, the three numbers are:
First number: 11
Second number: 3
Third number: 55