Ronnel spent 1/5 of his money to buy a food. He spent 1/4 of the remaining money to buy a magazine.If he had 360 pesos left in his wallet, how much money did he have at first?
Let's solve the problem step-by-step.
Let's assume Ronnel had x pesos at first.
Step 1: Ronnel spent 1/5 of his money to buy food.
He had 4/5 of his money remaining.
Money Remaining after buying food = (4/5) * x
Step 2: Ronnel spent 1/4 of the remaining money to buy a magazine.
He had 3/4 of the remaining money after buying the magazine.
Money Remaining after buying the magazine = (3/4) * (4/5) * x
Money Remaining after buying the magazine = (3/5) * x
According to the question, Ronnel had 360 pesos left in his wallet.
So, (3/5) * x = 360
To find the value of x, we need to isolate x on one side of the equation.
Multiplying both sides by 5/3, we get:
x = (360) * (5/3)
x = 600
Therefore, Ronnel had 600 pesos at first.
To solve this problem, we need to work backward. Let's start with the information given at the end.
We know that Ronnel had 360 pesos left in his wallet after buying the magazine.
Now, let's calculate how much money he had before buying the magazine.
If Ronnel spent 1/4 of the remaining money on the magazine, then he had 4 times the amount spent on the magazine. So, the money Ronnel had before buying the magazine was 4 * 360 = 1440 pesos.
Next, let's calculate how much money Ronnel had before buying the food.
If Ronnel spent 1/5 of his money on food, then he had 5 times the amount spent on food. So, the money Ronnel had before buying food was 5 * 1440 = 7200 pesos.
Therefore, Ronnel had 7200 pesos at first.
amount of original money ---- x
(1/5)x + (1/4)(4/5)x + 360 = x
x/5 + x/5 + 360 = x
times 5, the LCD
x + x + 1800 = 5x
3x = 1800
x = 600
check:
he spent 1/5 of 600, or 120 , leaving him with 480
he spend 1/4 of 480 on food, leaving him with 360