.I went to a store and spent 1/3 of my money and P5.00 more. Then, I went to a second store where I spent 3/5 of my remaining money plus P9.00 more. I had exactly P45.00 left. How much money had I at first?
m - m/3 - 5 - 3/5(m - m/3 - 5) - 9 = 45
m - m/3 - 3m/5 + m/5 = 56
15m - 5m - 9m + 3m = 840
To find out how much money you had at first, we can work backward from the information given. Let's break down the problem step by step:
1. Let's assume the amount of money you had at first is "x" pesos.
2. You spent 1/3 of your money in the first store, which is (1/3)*x pesos. You also spent P5.00 more, so the total spent in the first store is (1/3)*x + P5.00.
3. After spending in the first store, you have (x - (1/3)*x - P5.00) pesos left, which is 2/3 of your initial amount minus P5.00.
4. Next, you went to a second store where you spent 3/5 of your remaining money plus P9.00 more. So, you spent (3/5)*(2/3)*x + P9.00 in the second store.
5. After spending in the second store, you have [2/3 of your initial amount minus P5.00] minus [(3/5)*(2/3)*x + P9.00] pesos left, which is equal to P45.00.
Now, we can set up an equation to solve for the initial amount x:
[2/3*x - P5.00] - [(3/5)*(2/3)*x + P9.00] = P45.00
Simplifying the equation:
2/3*x - P5.00 - (3/5)*(2/3)*x - P9.00 = P45.00
2/3*x - P5.00 - (2/5)*x - P9.00 = P45.00
[(2/3)x - (2/5)x] - (P5.00 + P9.00) = P45.00
(10/15)x - (6/15)x - P14.00 = P45.00
(4/15)x - P14.00 = P45.00
(4/15)x = P45.00 + P14.00
(4/15)x = P59.00
To solve for x, we can multiply both sides of the equation by (15/4):
x = P59.00 * (15/4)
Calculating the value of x:
x ≈ P221.25
Therefore, you had approximately P221.25 at first.