The sum of two numbers is 74. The larger number is 3 more than the smaller number. Find the numbers. i need to use substition method
L+S=74
L=S+3
S+3 + S=74
2S+3=74
2S=71
S=35.5
L= 38.5
To solve this problem using the substitution method, we will assign variables to the unknown values in the problem.
Let's assume the smaller number is "x" and the larger number is "y".
Based on the given information, we can form two equations:
Equation 1: The sum of two numbers is 74.
x + y = 74
Equation 2: The larger number is 3 more than the smaller number.
y = x + 3
Now, we can solve this system of equations by substituting Equation 2 into Equation 1:
x + (x + 3) = 74
Combine like terms:
2x + 3 = 74
Subtract 3 from both sides:
2x = 74 - 3
2x = 71
Divide both sides by 2:
x = 71/2
x = 35.5
Now that we have found the value for "x," we can substitute it back into one of the original equations to find the value of "y":
y = x + 3
y = 35.5 + 3
y = 38.5
So, the smaller number is 35.5 and the larger number is 38.5, which sums up to 74.