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?
(A) ₱2,350
(B) ₱3,525
(C) ₱2,820
(D ₱1,180
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.}}
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.
Your method and answer are correct. I apologize for the mistake in my previous response. Billy has approximately ₱2,350.
Let's assume the amount of money Billy has to be "x" pesos.
According to the given information, two-thirds of Billy's money is equal to five-sixth of Zander's money. Mathematically, this can be represented as:
(2/3) * x = (5/6) * (4230 - x)
To solve this equation, we can first simplify the right side:
(2/3) * x = (5/6) * (4230 - x)
Multiply both sides by 6 to remove the fractions:
2 * 6 * x = 5 * (4230 - x)
12x = 21150 - 5x
Combine like terms:
12x + 5x = 21150
17x = 21150
Divide both sides by 17:
x = 21150 / 17
x ≈ 1244.12
Therefore, Billy has approximately ₱1244.12.
Considering the options given, the closest amount to ₱1244.12 is option (D) ₱1,180.
So, the answer is ₱1,180.