One number is 3 more that half of a second number. If the average of the two numbers is 31/2, find the smaller of the two numbers.
PLEASE HELP. thanks!
N-3=1/2 S
N+S= 2*(31 1/2)
help me
To solve this problem, we can use a system of equations. Let's let the first number be N and the second number be S.
From the given information, we can set up two equations:
1. "One number is 3 more than half of a second number": N = (1/2)S + 3
2. "The average of the two numbers is 31/2": (N + S) / 2 = 31/2
Now we have a system of equations with two unknowns (N and S), and we can solve it using substitution or elimination.
Let's use substitution method to solve the system:
First, we can substitute the value of N from equation 1 into equation 2:
((1/2)S + 3 + S) / 2 = 31/2
Next, we simplify the equation:
(3/2)S + 3 = 31/2
Now, we can multiply both sides of the equation by 2 to get rid of the fraction:
3S + 6 = 31
Subtract 6 from both sides:
3S = 25
Divide both sides by 3:
S = 25/3
So, the second number is 25/3.
To find the smaller of the two numbers, we can substitute the value of S back into equation 1:
N = (1/2)(25/3) + 3
N = 25/6 + 3
N = (25 + 18)/6
N = 43/6
So, the smaller of the two numbers is 43/6.
Therefore, the smaller number is 43/6.
I hope this helps! Let me know if you have any further questions.