The sum of two numbers is 46 the sum of 6 times the larger and 5 times the smaller is 259 find the numbers
Let's assume the larger number is x and the smaller number is y.
From the problem, we know that:
x + y = 46 (Equation 1)
We're also given that:
6x + 5y = 259 (Equation 2)
We can solve this system of equations by substitution or elimination. Let's use the substitution method here.
From Equation 1, we can express x in terms of y:
x = 46 - y
Plugging this into Equation 2, we get:
6(46 - y) + 5y = 259
Simplifying this equation gives:
276 - 6y + 5y = 259
-1y = -17
y = 17
Plugging this value of y into Equation 1:
x + 17 = 46
x = 46 - 17
x = 29
Therefore, the larger number is 29 and the smaller number is 17.