Ronnel spent 1/5 of his money to buy food. He then spent 1/4 of the remaining money to buy magazine. If he had ₱360.00 left in his wallet, how much money did he have at first?
Let the money he had at first be x
Then let be straight forward i.e
1/5x+(1/4×4/5)x=1
Then.1/5x+1/5x=1
Then.2/5x=1
We can say 1-2/5x= 3/5x
Then 3/5x=360
Now x=360×5÷3=600
Well, if Ronnel had ₱360.00 left in his wallet after buying food and a magazine, we can work backward to figure out how much money he had at first.
Let's start with the ₱360.00 left in his wallet. This represents 3/4 of the remaining money after buying the magazine.
To find the total remaining money, we can divide ₱360.00 by 3/4:
₱360.00 ÷ (3/4) = ₱360.00 × (4/3) = ₱480.00
So, Ronnel had ₱480.00 left after buying the magazine. This ₱480.00 represents 4/5 of his money at that point.
To find the total money Ronnel had before buying the magazine, we can divide ₱480.00 by 4/5:
₱480.00 ÷ (4/5) = ₱480.00 × (5/4) = ₱600.00
Therefore, Ronnel had ₱600.00 at first. I hope this doesn't make your head spin like a merry-go-round!
Let's assume Ronnel had x amount of money at first.
Step 1: Ronnel spent 1/5 of his money to buy food, leaving him with 4/5 of his money.
Amount remaining after buying food = (4/5) * x
Step 2: Ronnel spent 1/4 of the remaining money to buy a magazine, leaving him with 3/4 of the remaining money.
Amount remaining after buying magazine = (3/4) * (4/5) * x
According to the given information, Ronnel had ₱360.00 left in his wallet after buying the magazine.
So, (3/4) * (4/5) * x = ₱360.00
Simplifying, (3/5) * x = ₱360.00
Multiplying both sides by 5/3 to isolate x, we get
x = (₱360.00 * 5) / 3
x = ₱600.00
Therefore, Ronnel had ₱600.00 at first.
To solve this problem, we can work backwards to find the original amount of money Ronnel had in his wallet before spending any money.
Let's start with the money he had left in his wallet, which is ₱360.00.
Ronnel spent 1/4 of the remaining money on a magazine, so we need to find the money he had before buying the magazine. Let's assign a variable to represent this amount.
Let's call the money he had before buying the magazine as "M2".
We know that Ronnel had ₱360.00 left after buying the magazine, so we can set up the equation:
M2 - (1/4)M2 = ₱360.00
Now, let's simplify the equation:
(3/4)M2 = ₱360.00
To isolate M2, we can multiply both sides of the equation by the reciprocal of (3/4), which is (4/3):
M2 = (₱360.00) * (4/3)
M2 = ₱480.00
Now we know that Ronnel had ₱480 before buying the magazine.
Next, Ronnel spent 1/5 of his money on food. We need to find the money he had before buying the food. Let's assign a variable to represent this amount.
Let's call the money he had before buying the food as "M1".
We know that Ronnel had ₱480.00 before buying the magazine, so we can set up the equation:
M1 - (1/5)M1 = ₱480.00
Now, let's simplify the equation:
(4/5)M1 = ₱480.00
To isolate M1, we can multiply both sides of the equation by the reciprocal of (4/5), which is (5/4):
M1 = (₱480.00) * (5/4)
M1 = ₱600.00
Therefore, Ronnel had ₱600.00 in his wallet at first.
Let n be the amount Ronnel started with. After he spent 1/5, he had 4/5 left. Similarly, he had 3/4ths of that amount after more spending. All told, he had:
(4/5 x 3/4)n=360
(3/5)n=360
n=360/(3/5)=600 to start with
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