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Alice can solve x sudoku puzzles in 4 hours and Betty can Y sudoku puzzles in 5 hours. Both of them can solve (3y-x-1) Sudoku puzzles in 3 hours. Alice and Betty can solve 7 sudoku puzzles in 1 hour. Find the difference in the number of Sudoku Puzzles at which Alice and Betty can solve in 1 hour.

User Spnkr
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Answer:

To find the difference in the number of Sudoku puzzles that Alice and Betty can solve in 1 hour, we need to compare their individual rates of puzzle-solving.

Let's start by finding the rates at which Alice and Betty can solve Sudoku puzzles:

Alice can solve x Sudoku puzzles in 4 hours, so her rate of solving is x puzzles per 4 hours, which can be simplified to (x/4) puzzles per hour.

Betty can solve y Sudoku puzzles in 5 hours, so her rate of solving is y puzzles per 5 hours, which can be simplified to (y/5) puzzles per hour.

Now, let's use the given information that both Alice and Betty can solve (3y-x-1) Sudoku puzzles in 3 hours.

We can set up the equation:

(3y-x-1) puzzles / 3 hours = 7 puzzles / 1 hour

Simplifying the equation:

(3y-x-1) / 3 = 7

Multiplying both sides by 3:

3y-x-1 = 7 * 3

Simplifying:

3y-x-1 = 21

Now, let's solve for x:

x = 3y - 22

Now that we have the relationship between x and y, we can find the rates of puzzle-solving for Alice and Betty:

Alice's rate: (x/4) puzzles per hour

Betty's rate: (y/5) puzzles per hour

To find the difference in the number of Sudoku puzzles they can solve in 1 hour, we subtract Betty's rate from Alice's rate:

Difference = Alice's rate - Betty's rate

Difference = (x/4) - (y/5)

Substituting the value of x:

Difference = ((3y - 22)/4) - (y/5)

Now, let's simplify the equation:

Difference = (15(3y - 22)/60) - (12y/60)

Difference = (45y - 330)/60 - (12y/60)

Difference = (45y - 330 - 12y)/60

Difference = (33y - 330)/60

Therefore, the difference in the number of Sudoku puzzles that Alice and Betty can solve in 1 hour is (33y - 330)/60.

User Wishmaster
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