Three times one number added to two times another give 34. The sum of the two number is 13 .find the numbers? Solutions
x+y = 13
3x+2y = 34
Now just solve for x and y.
To solve this problem, let's assign variables to the two unknown numbers. Let's say the first number is x and the second number is y.
According to the information given, three times one number (x) added to two times another (y) gives 34. This can be represented as the equation:
3x + 2y = 34 (Equation 1)
It is also given that the sum of the two numbers is 13. This can be represented as:
x + y = 13 (Equation 2)
Now, we have a system of two equations with two variables. To solve this system, we can use substitution or elimination method. Let's use the elimination method.
We can multiply Equation 2 by 3 to make the coefficients of x in both equations equal:
3(x + y) = 3(13)
3x + 3y = 39 (Equation 3)
Now, we can subtract Equation 3 from Equation 1 to eliminate the x variable:
(3x + 2y) - (3x + 3y) = 34 - 39
3x - 3x + 2y - 3y = -5
- y = -5
y = 5
Now, substitute y = 5 into Equation 2 to solve for x:
x + 5 = 13
x = 13 - 5
x = 8
So, the two numbers are 8 and 5.