SOLUTION: Rama was getting some items for the new school year. First, he bought some textbooks with $8 more than 1/3 of his money. Next, Next, he bought his stationery with $12.20 less than

Question 1209350: Rama was getting some items for the new school year. First, he bought some textbooks with $8 more than 1/3 of his money. Next, Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. Then, he had $15.40 with him. How much money did he have at first?
Found 4 solutions by proyaop, mccravyedwin, greenestamps, MathTherapy:
Answer by proyaop(69)   (Show Source): You can put this solution on YOUR website!
**1. Let's represent:**
* The initial amount of money Rama had as 'x'
**2. Formulate the equation:**
* **Textbooks:** Rama spent (x/3) + 8 dollars on textbooks.
* **Remaining money after textbooks:** x - (x/3) - 8 = (2/3)x - 8
* **Stationery:** Rama spent 1/2 * ((2/3)x - 8) - 12.20 dollars on stationery.
* **Remaining money after stationery:** (2/3)x - 8 - 1/2 * ((2/3)x - 8) + 12.20 = (2/3)x - 8 - (1/3)x + 4 + 12.20 = (1/3)x + 8.20
* **School Socks:** Rama spent 1/2 * ((1/3)x + 8.20) + 2.80 dollars on socks.
* **Remaining money:** (1/3)x + 8.20 - 1/2 * ((1/3)x + 8.20) - 2.80 = 15.40
**3. Simplify and solve the equation:**
* (1/3)x + 8.20 - (1/6)x - 4.10 - 2.80 = 15.40
* (1/6)x + 1.30 = 15.40
* (1/6)x = 14.10
* x = 14.10 * 6
* x = 84.60
**Therefore, Rama had $84.60 at first.**

Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

Looks like AI got this one correct. AI will get better and better, but you can't trust it with everything yet. There is still some use for us humans. So I'll do it the human way. ------------ Rama was getting some items for the new school year. Let x = the amount at first. First, he bought some textbooks with $8 more than 1/3 of his money. Let y = how much he had left after buying textbooks. Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. Let z = how much he had left after buying stationery. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. Let w = how much he had left after buying socks. Then, he had $15.40 with him. How much money did he have at first? Substitute the 4th equation in the 3rd equation Substitute that in the 2nd equation Substitute that in the 1st equation Answer: $84.60 <--SOLUTION! Checking: He had $84.60 First, he bought some textbooks with $8 more than 1/3 of his money. 1/3 of his 84.60 or 28.20, plus 8 is 36.20, which was what he spent, so he had 84.60-36.20 or 48.40 left. Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. 1/2 of his remaining money was 1/2 of 48.40, or 24.20, minus 12.20, or 12, which was what he spent, so he had 48.40-12 or 36.40 left. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. 1/2 of his remaining money was 1/2 of 36.40, or 18.20, plus 2.80, or 21, which was what he spent, so he had 36.40-21 or 15.40 left. Then, he had $15.40 with him. So now we know we have the right answer, $84.60. Edwin

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Working the problem "forwards", as shown in the other responses, requires doing some back-substitution to get the final answer.

You can get the answer directly by working the problem backwards.

He finished with $15.40 after spending $2.80 more than half of his money on school socks.

let x = amount he had before buying the socks

Before buying the socks, the amount he had was $36.40. That was what he had after spending $12.20 less than half his money on stationery.

let y = amount he had before buying the stationery

The amount he had before buying the stationery was $48.40. That was what he had after spending $8 more than 1/3 of his money on textbooks.

let z = amount he had before buying the textbooks (i.e., the amount he had at first)

ANSWER: The amount he started with was $86.40

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Rama was getting some items for the new school year. First, he bought some textbooks with $8 more than 1/3 of his money. Next, Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. Then, he had $15.40 with him. How much money did he have at first? Let original amount he had be M Remainder after spending $8 more than of his money: - 8 = Remainder after spending $12.20 less than of his 1^st REMAINDER: = = Remainder after spending $2.80 less than of his 2^nd REMAINDER: = = Since his last (3^rd) REMAINING amount was , which was given as $15.4, we get: Cross-multiplying, we get original amount he had, or M as: 6(14.1) = $84.60

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