The sum of money of Billy and Zander is ₱4,230. If two-thirds of Billy's money is equal to five-sixth of Zander's money, how much money does Billy have?

Question

(A) ₱2,350
(B) ₱3,525
(C) ₱2,820
(D ₱1,180

Answer 1

Let's assume that Billy has the amount of money represented by x.
Zander will have 2/3 * x = 5/6 * (4230 - x) = 5/6 * 4230 - 5/6 * x.
Multiplying 6 on both sides of 2/3 * x = 5/6 * 4230 - 5/6 * x, we get 4x = 5 * 4230 - 5 * x.
Multiplying both sides by -1, we get -5x + 4x = -5 * 4230.
This simplifies to -x = -5 * 4230.
Dividing both sides by -1, we get x = 5 * 4230.
So, Billy has x = 5 * 4230 = ₱21,150.
Therefore, Billy has ₱21,150. Answer: \boxed{\text{(E)} \text{ None of these.}}

Answer 2

To solve this problem, we can set up a system of equations based on the given information. Let's denote Billy's money as B and Zander's money as Z.

According to the problem, the sum of Billy and Zander's money is ₱4,230. Therefore, we have the equation:

B + Z = 4,230 ----(1)

It is also stated that two-thirds of Billy's money is equal to five-sixth of Zander's money. Mathematically, this can be expressed as:

(2/3)B = (5/6)Z

To simplify this equation, we can multiply both sides by 6 to eliminate the fractions:

6 * (2/3)B = 6 * (5/6)Z
4B = 5Z

Now we have a second equation:

4B = 5Z ----(2)

We can solve this system of equations using substitution or elimination method. Let's use substitution method here.

From equation (2), we can express Z in terms of B:

Z = (4/5)B

Substituting this value of Z into equation (1), we get:

B + (4/5)B = 4,230
(9/5)B = 4,230

To isolate B, we can multiply both sides by (5/9):

(5/9) * (9/5)B = (5/9) * 4,230
B = (5/9) * 4,230

Calculating this expression gives us:

B ≈ ₱2,350

Therefore, Billy has approximately ₱2,350.

The correct answer is option (A) ₱2,350.

Answer 3

Your method and answer are correct. I apologize for the mistake in my previous response. Billy has approximately ₱2,350.