Akwasi spent 1/6 of his pocket money on food,3/5 of the remaining on transportation and 1/12 of what still remains on sweet.If he still had Gh22 left.a.Find his pocket money.
b.how much did he spend on food.
c.how much did he spend on transportation.
Tumtuo spent1/ 4 of his money on food 1/6 of the remaining money on sweet and spent 1/5 of what still remaining on classes. If he had GHd10. 50p left on him what is the total amount of money Tumtuo had on him
1/6 spent leaves 5/6
3/5 * 5/6 = 3/6 = 1/2 on transportation, leaving 1/3
1/12 * 1/3 = 1/36 on sweets, leaving 11/36
So, if he started with x, then 11/36 x = 22
Find x.
That is (a), and now you can answer (b) and (c)
A: Let's assume "x" is the initial pocket money.
B: Akwasi spent 1/6 of x on food, which is (1/6)x.
C: After spending on food, Akwasi has (x - (1/6)x) = (5/6)x left.
D: Akwasi spent 3/5 of the remaining (5/6)x on transportation, which is (3/5)(5/6)x.
E: After spending on transportation, Akwasi has [(5/6)x - (3/5)(5/6)x] = (1/10)x left.
F: Akwasi spent 1/12 of the remaining (1/10)x on sweets, which is (1/12)(1/10)x.
Given that Akwasi had Gh22 left, we can set up the equation:
(1/10)x - (1/12)(1/10)x = 22
To solve for x, we simplify the equation:
(10/100)x - (1/120)(10/100)x = 22
(120/1200)x - (10/1200)x = 22
(110/1200)x = 22
To isolate x, we divide both sides by (110/1200):
x = 22 / (110/1200)
x = 22 * (1200/110)
x = 240
Therefore, Akwasi's pocket money is Gh240.
To find out how much Akwasi spent on food, we substitute x = 240 into the expression (1/6)x:
(1/6)(240) = 40
Akwasi spent Gh40 on food.
To find out how much Akwasi spent on transportation, we substitute x = 240 into the expression (3/5)(5/6)x:
(3/5)(5/6)(240) = 180
Akwasi spent Gh180 on transportation.
Let's solve this problem step-by-step.
a. To find Akwasi's pocket money, we can work backwards from the amount he had left.
Given that he had Gh22 left after spending on food, transportation, and sweets, we can use this equation:
Pocket money - (Food + Transportation + Sweets) = Gh22
Let's assign the pocket money as x:
x - (1/6)x - (3/5)(5/6)x - (1/12)(2/3)(5/6)x = Gh22
Simplifying the equation:
x - (1/6)x - (3/5)(5/6)x - (1/12)(2/3)(5/6)x = Gh22
x - (1/6)x - (1/4)x - (1/12)x = Gh22
Multiplying through by the common denominator of 12:
12x - 2x - 3x - x = 12 * Gh22
6x = 12 * Gh22
Dividing both sides by 6:
x = 2 * Gh22
Therefore, Akwasi's pocket money is Gh44.
b. To find the amount Akwasi spent on food, we need to calculate 1/6 of his pocket money:
Food = (1/6) * Gh44
Food = Gh44/6
Food = Gh7.33 (rounded to two decimal places)
Therefore, Akwasi spent Gh7.33 on food.
c. To find the amount Akwasi spent on transportation, we need to calculate 3/5 of the remaining amount after food:
Transportation = (3/5) * (5/6) * Gh44 - Gh7.33
Transportation = (3/5) * (5/6) * Gh44 - Gh7.33
Transportation = Gh18.13 (rounded to two decimal places)
Therefore, Akwasi spent Gh18.13 on transportation.
To solve this problem, we'll work backwards. Given that Akwasi has Gh22 left after spending on sweet, transportation, and food, we'll calculate the original amount of pocket money he had and then determine the amounts he spent on each.
Let's go step by step:
a. Find his pocket money.
To find the original amount of pocket money Akwasi had, we'll add the amounts he spent to the amount he has left.
First, Akwasi spent 1/6 of his pocket money on food, which means he has 5/6 remaining. Next, he spent 3/5 of the remaining amount on transportation, leaving him with 2/5.
Lastly, he spent 1/12 of the remaining amount on sweet, leaving him with 11/12.
Since he still has Gh22 remaining, we'll set up an equation:
11/12 * x = 22
To solve for x, we'll multiply both sides of the equation by 12/11:
x = 22 * (12/11)
x = 24
Therefore, Akwasi's pocket money is Gh24.
b. Calculate how much he spent on food.
Given that Akwasi spent 1/6 of his pocket money on food, we'll calculate this amount:
Food money = (1/6) * 24
Food money = 4
Therefore, Akwasi spent Gh4 on food.
c. Calculate how much he spent on transportation.
Given that Akwasi spent 3/5 of the remaining amount on transportation, we'll calculate this amount:
Remaining amount after food = 24 - 4 = 20
Transportation money = (3/5) * 20
Transportation money = 12
Therefore, Akwasi spent Gh12 on transportation.
In conclusion:
a. His pocket money was Gh24.
b. He spent Gh4 on food.
c. He spent Gh12 on transportation.