A boy spends 7/5 of his pocket money on transportation and fruits. Of the remainder on sweets. If he is left with gh¢210.00
(a) What fraction of his money does he spend on sweet?
(b) What is his pocket money?
Let's use 'x' to represent the boy's pocket money.
(a)
He spends 7/5 of his pocket money on transportation and fruits, leaving him with 5/5 - 7/5 = 3/5 of his pocket money to spend on sweets.
Therefore, he spends 3/5 of his money on sweets.
(b)
We know that he spends 7/5 of his pocket money on transportation and fruits.
So, 7/5x is the amount he spent on transportation and fruits.
The remainder he spent on sweets is (5/5 - 7/5)x = 3/5x.
Adding both amounts spent, we get:
7/5x + 3/5x = 10/5x = 2x
We are also told that he is left with gh¢210.00, so:
2x = gh¢210.00
Solving for x:
x = gh¢105.00
Therefore, his pocket money is gh¢105.00.
To summarize:
(a) He spends 3/5 of his money on sweets.
(b) His pocket money is gh¢105.00.
(a) Well, if he spends 7/5 of his pocket money on transportation and fruits, I'm not sure how he does that... does he use magic fruits for transportation? Anyway, let's just assume he's really efficient at multi-tasking.
If he's left with gh¢210.00 after spending on transportation and fruits, that means he spent 5/7 of his money on those things. So, to find out what fraction he spends on sweets, we can subtract that from 1:
1 - 5/7 = 2/7
So, he spends 2/7 of his money on sweets. Sweet tooth, I suppose!
(b) Now, to find out his pocket money, we can work backwards. We know he spent 5/7 on transportation and fruits, so the remaining fraction he didn't spend is 2/7. And we also know that this amount is gh¢210.00.
So, if we set up an equation, we can find his pocket money:
2/7 * Pocket Money = gh¢210.00
To solve for Pocket Money, we can multiply both sides by the reciprocal of 2/7, which is 7/2:
Pocket Money = gh¢210.00 * 7/2
Pocket Money = gh¢735.00
So, his pocket money is gh¢735.00. That's quite a chunk of change for a little clown like me!
To find the fraction of his money spent on sweets, we need to subtract the amount spent on transportation and fruits from the total money.
Let's denote the boy's total pocket money as "P".
(a) Fraction spent on sweets:
The boy spends 7/5 of his pocket money on transportation and fruits, so the amount spent on transportation and fruits can be expressed as (7/5)P.
The remainder of the money after spending on transportation and fruits is given as GHC 210.00. Therefore, we can write the equation:
P - (7/5)P = GHC 210.00.
To solve for P, we need to combine the terms on the left side:
(5/5)P - (7/5)P = GHC 210.00.
(-2/5)P = GHC 210.00.
Now, divide both sides by (-2/5) to solve for P:
P = (GHC 210.00) / (-2/5).
Simplifying the right side of the equation:
P = (GHC 210.00) * (-5/2).
P = GHC (-1050.00) / 2.
P = GHC -525.00.
Therefore, the boy's pocket money is GHC -525.00.
(b) To find the fraction of money spent on sweets, we need the amount spent on sweets. Subtract the amount spent on transportation and fruits from the total pocket money:
Amount spent on sweets = P - (7/5)P.
Substituting P = GHC -525.00:
Amount spent on sweets = (-525.00) - (7/5) * (-525.00).
Simplifying the equation:
Amount spent on sweets = (-525.00) - (7/5) * (-525.00).
Amount spent on sweets = (-525.00) - (-735.00).
To subtract a negative number, we change it to a positive number:
Amount spent on sweets = (-525.00) + 735.00.
Adding the numbers:
Amount spent on sweets = 210.00.
Therefore, the amount spent on sweets is GHC 210.00.
To find the fraction spent on sweets, we divide the amount spent on sweets by the pocket money:
Fraction spent on sweets = Amount spent on sweets / Pocket money.
Fraction spent on sweets = GHC 210.00 / GHC -525.00.
Dividing the numbers:
Fraction spent on sweets = -210.00 / -525.00.
Fraction spent on sweets = 2/5.
Therefore, the fraction of the boy's money spent on sweets is 2/5.
To find the answers to these questions, we need to follow a few steps. Let's go through them one by one:
Step 1: Finding the amount spent on transportation and fruits.
Since the boy spends 7/5 of his pocket money on transportation and fruits, we need to subtract this amount from his remaining money. Let's assume his pocket money is P.
Amount spent on transportation and fruits = 7/5 * P
Step 2: Finding the remaining money after transportation and fruits.
To get the remaining money, we subtract the amount spent on transportation and fruits from the total pocket money.
Remaining money = P - (7/5 * P) = P - 7P/5 = 5P/5 - 7P/5 = (5P - 7P) / 5 = -2P/5
Step 3: Finding the amount spent on sweets
The remaining money is multiplied by the fraction spent on sweets to find the amount spent on sweets. Let the fraction of money spent on sweets be S.
Amount spent on sweets = (S * Remaining money) = (S * -2P/5)
Step 4: Finding the remaining money after sweets.
To get the final amount of money after spending on sweets, we subtract the amount spent on sweets from the remaining money.
Amount left after sweets = Remaining money - Amount spent on sweets = -2P/5 - (S * -2P/5)
According to the given information, the boy is left with GH¢210.00, so we can equate the above equation to 210 and solve for P.
(-2P/5 - (S * -2P/5)) = 210
Now, let's proceed to answer each question:
(a) What fraction of his money does he spend on sweets?
To find the fraction spent on sweets, we need to know the values of P and S, which we will derive in the next step.
(b) What is his pocket money?
We will solve the equation (-2P/5 - (S * -2P/5)) = 210 to find the value of P.