the sum of two numbers is 38 . the larger number is 11 more than the half of the smaller number. what are the two numbers? (12,26) (14,24) (18,20) (19,21)
Let's assume the two numbers are x and y. We know that:
1. x + y = 38 (the sum of the two numbers is 38).
2. x = (1/2)*y + 11 (the larger number is 11 more than half of the smaller number).
To find the values of x and y, we can solve these two equations simultaneously.
Substituting the second equation into the first equation:
(1/2)*y + 11 + y = 38
Simplifying:
(3/2)*y + 11 = 38
(3/2)*y = 38 - 11
(3/2)*y = 27
y = (2/3)*27
y = 18
Substituting the value of y into the second equation:
x = (1/2)*18 + 11
x = 9 + 11
x = 20
Therefore, the two numbers are 18 and 20. Thus, the correct answer is (18, 20).
To solve this problem, we can set up a system of equations based on the given information.
Let's say the smaller number is 'x' and the larger number is 'y'. According to the problem, we have two pieces of information:
1. The sum of the two numbers is 38:
x + y = 38
2. The larger number is 11 more than half of the smaller number:
y = (1/2)x + 11
To find the values of 'x' and 'y', we can solve this system of equations.
One way to solve it is by substitution. From equation 2, we can isolate 'x':
y = (1/2)x + 11
Multiply both sides by 2:
2y = x + 22
Rearrange the equation:
x = 2y - 22
Now, substitute this value of 'x' into equation 1:
x + y = 38
(2y - 22) + y = 38
Combine like terms:
3y - 22 = 38
Add 22 to both sides:
3y = 60
Divide both sides by 3:
y = 20
Now, substitute this value of 'y' back into equation 1 to find 'x':
x + 20 = 38
Subtract 20 from both sides:
x = 18
So, the two numbers are 18 and 20. Therefore, the correct answer is (18, 20).
x + 0.5x + 11 = 38
1.5x = 27
x = 18