Hamlet and Ophelia had stickers in the ratio 4:7. Hamlet gave 27 stickers to Ophelia, who gave 45 stickers to Claudius. The sum of Hamlet and Ophelia’s stickers became 153 more than the number of stickers Claudius had. Claudius then gave 2/9 of her stickers to Hamlet and 1/4 of her remaining to Ophelia. In the end, the sun of Hamlet and Claudius’s stickers was 71 more than Ophelia’s. How many stickers did Ophelia have at first?

Question

Hamlet and Ophelia had stickers in the ratio 4:7. Hamlet gave 27 stickers to Ophelia, who gave 45 stickers to Claudius. The sum of Hamlet and Ophelia’s stickers became 153 more than the number of stickers Claudius had. Claudius then gave 2/9 of her stickers to Hamlet and 1/4 of her remaining to Ophelia. In the end, the sun of Hamlet and Claudius’s stickers was 71 more than Ophelia’s. How many stickers did Ophelia have at first?

Answer 1

Hamlet's number --- 4x

Ophelia's number --- 7x
Claudias number ---- y

after 1st exchange:
Hamlet: 4x-27
Ophelia: 7x+27 - 45 = 7x - 18
Claudius: y + 45
so: (4x-27) + (7x-18) - (y+45) = 153
11x - y = 63 or y = 11x - 63

after 2nd exchange:
Hamlet: 4x-27 + (2/9)(y+45)
Ophelia: 7x-18 + (1/4)(7/9)(y+45)
= 7x - 18 + (7/36)y + 35/4
= (1/36)(252x + 7y - 333)
Claudius: y+45 - (1/4)(7/9)(y+45) - ( (7/36)y + 35/4 )
= (11y + 495)/18

4x-27 + (2/9)(y+45) + (11y + 495)/18 - (1/36)(252x + 7y - 333) = 71
which I got to reduce to
108 x + 1845 = 23y , now sub in y = 11x - 63
108x + 1845 = 23(11x - 63)
which I solved to get
x = 3294/745
ARGGGHHHHHH!!!! The answers should clearly be a whole number.

There has to be an error somewhere, I trust my method.

Answer 2

Was going to add that

Something is rotten in the state of Denmark

Answer 3

To solve this problem, let's break it down step by step.

Step 1: Determine the sticker ratio between Hamlet and Ophelia.
Hamlet and Ophelia had stickers in the ratio 4:7, which means for every 4 stickers Hamlet had, Ophelia had 7.

Step 2: Calculate the initial number of stickers Ophelia had.
Let's assume Hamlet had 4x stickers and Ophelia had 7x stickers. Since they had a total of 11x stickers, we can say that their total number of initial stickers was 11x.

Step 3: Calculate the number of stickers Hamlet gave to Ophelia.
Hamlet gave 27 stickers to Ophelia. Since we assumed Hamlet had 4x stickers, he gave away 27 out of 4x stickers, which can be written as (27/4x).

Step 4: Calculate the number of stickers Ophelia gave to Claudius.
Ophelia gave 45 stickers to Claudius. Since Ophelia had 7x stickers, she gave away 45 out of 7x stickers, which can be written as (45/7x).

Step 5: Calculate the remaining number of stickers Hamlet and Ophelia had.
After Hamlet gave 27 stickers to Ophelia, Hamlet had (4x - 27) stickers remaining.
After Ophelia gave 45 stickers to Claudius, Ophelia had (7x - 45) stickers remaining.

Step 6: Evaluate the condition that Hamlet and Ophelia's total stickers became 153 more than Claudius's stickers.
According to the problem, the sum of Hamlet and Ophelia's stickers became 153 more than the number of stickers Claudius had. So we can write the equation as:
(4x - 27) + (7x - 45) = (45 + 27) + 153.

Step 7: Simplify and solve the equation to find the value of x.
11x - 72 = 225 + 153.
11x = 450 + 72.
11x = 522.
x = 47.45454545 (approximately).

Since x represents the number of stickers Ophelia had in the ratio, we can round it to the nearest whole number:
x ≈ 47.

So, Ophelia initially had 7x stickers, which is approximately 7 * 47 = 329 stickers. Therefore, Ophelia initially had 329 stickers.