The sum of two positive numbers is 34. When the smaller number is subtracted from twice the larger, the result is 26. Find the two numbers,
smaller --- x
larger ---- 34-x
2(34-x) - x = 26
easy to solve for x
System of Equations
Let x: smaller y: larger
x + y = 34
2y - x = 26
Using elimination to solve the system yields 3y = 60. Thus y = 20, so x =14
To solve this problem, let's use a system of equations:
Let's assume that the smaller number is represented by 'x', and the larger number is represented by 'y'.
From the given information, we can form two equations:
1. The sum of two positive numbers is 34:
x + y = 34
2. When the smaller number is subtracted from twice the larger, the result is 26:
2y - x = 26
Now, we can solve this system of equations using substitution or elimination.
Let's use substitution method:
From equation 1, we have x = 34 - y
Now, substitute x in equation 2:
2y - (34 - y) = 26
Simplify the equation:
2y - 34 + y = 26
Combine like terms:
3y - 34 = 26
Add 34 to both sides:
3y = 60
Divide both sides by 3:
y = 20
Now, substitute the value of y back into equation 1:
x + 20 = 34
Subtract 20 from both sides:
x = 14
So, the smaller number is 14, and the larger number is 20.