sum of two numbers is 26. the sum of 5 times the larger and 6 times the smaller is 134. find the numbers.
Let's assume the larger number is x and the smaller number is y.
We have two equations from the given information:
1. x + y = 26 (equation 1)
2. 5x + 6y = 134 (equation 2)
Multiplying equation 1 by 5, we get:
5(x + y) = 5(26)
5x + 5y = 130
Now we can subtract equation 2 from the result:
(5x + 5y) - (5x + 6y) = 130 - 134
5x + 5y - 5x - 6y = -4
Simplifying the equation gives:
-y = -4
y = 4
Substituting the value of y into equation 1 gives us:
x + 4 = 26
x = 26 - 4
x = 22
So, the two numbers are 22 and 4.