24. The sum of two numbers is twice their
difference. If difference of the numbers is p,
find the larger number.
A. p/2
B. 3p/2
C. 5p12
D. 3p
Let the larger number be x and the smaller number be y.
The sum of two numbers is twice their difference can be written as:
x + y = 2(x - y)
Simplifying this equation, we get:
x + y = 2x - 2y
3y = x
Since we are given that the difference of the numbers is p, we can write the equation as:
x - y = p
Substituting x = 3y into this equation, we get:
3y - y = p
2y = p
y = p/2
Therefore, the larger number (x) is 3 times the smaller number (y):
x = 3y = 3 * (p/2) = 3p/2
The answer is B. 3p/2.
To solve this problem, let's assume the two numbers are A and B.
Given that the difference of the numbers is p, we can write the equation as:
A - B = p (1)
And since the sum of the numbers is twice their difference, we can write:
A + B = 2(A - B) (2)
To find the larger number, we need to solve these equations.
To do that, let's simplify equation (2) by expanding the right side:
A + B = 2A - 2B
Move the B terms to the left side and the A terms to the right side:
A - 2A = -2B - B
Combine like terms:
- A = -3B
Divide both sides by -3:
A = 3B
Now substitute this value of A in equation (1):
3B - B = p
Combine like terms:
2B = p
Divide both sides by 2:
B = p/2
Therefore, the larger number is B, which is equal to p/2.
So, the correct answer is:
A. p/2