the sum of two numbers is 74. one number is 11 more than half the other. find both numbers
x + 0.5x + 11 = 74
1.5x = 63
x = ?
74-m = m/2 + 11
63 = 3 m/2
m = 63*2/3
= 42
74 - 42 = 32
To find the two numbers, let's set up the equations using the given information.
Let's assume the first number is "x" and the second number is "y."
According to the problem, the sum of the two numbers is 74:
Equation 1: x + y = 74
It is also given that one number is 11 more than half the other:
Equation 2: x = (1/2)y + 11
Now we have a system of equations:
Equation 1: x + y = 74
Equation 2: x = (1/2)y + 11
To solve the system, we can substitute Equation 2 into Equation 1:
(1/2)y + 11 + y = 74
(3/2)y + 11 = 74
(3/2)y = 74 - 11
(3/2)y = 63
To isolate y, we can multiply both sides of the equation by 2/3:
y = (2/3) * 63
y = 42
Now substitute this value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
x + 42 = 74
x = 74 - 42
x = 32
So the two numbers are x = 32 and y = 42.