Ryan and Daisy have a total of 60 stamps. If Ryan gives 10 stamps to Daisy, the number of stamps Daisy has is 5 times of Ryan. Find the number of stamps that Ryan originally has.
Understand the Problem
The question is asking to find the number of stamps that Ryan originally has based on the total number of stamps he and Daisy have, along with the conditions related to the transfer of stamps between them.
Answer
Ryan originally has $20$ stamps.
Answer for screen readers
Ryan originally has ( r = 20 ) stamps.
Steps to Solve
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Define variables for the number of stamps
Let ( r ) be the number of stamps Ryan originally has, and ( d ) be the number of stamps Daisy originally has. -
Set up the total stamps equation
According to the problem, Ryan and Daisy together have 60 stamps: $$ r + d = 60 $$ -
Adjust for the stamp transfer
Ryan gives 10 stamps to Daisy. After the transfer:
- Ryan now has ( r - 10 )
- Daisy now has ( d + 10 )
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Set up the relationship after the transfer
The problem states that after the transfer, Daisy has 5 times as many stamps as Ryan: $$ d + 10 = 5(r - 10) $$ -
Simplify the equation
Substituting ( d ) from the first equation into the second: Using ( d = 60 - r ): $$ (60 - r) + 10 = 5(r - 10) $$ -
Solve for ( r )
Let's simplify: $$ 70 - r = 5r - 50 $$ Combine like terms: $$ 70 + 50 = 5r + r $$ $$ 120 = 6r $$ Divide both sides by 6: $$ r = 20 $$ -
Calculate ( d )
Using the total stamps equation: $$ d = 60 - r = 60 - 20 = 40 $$
Ryan originally has ( r = 20 ) stamps.
More Information
Ryan's final count after giving 10 stamps to Daisy means he ends up with 10 stamps, while Daisy, initially having 40 stamps, ends up with 50.
Tips
- Incorrectly setting up the relationship after the transfer.
- Forgetting to substitute back into the equations or miscalculating the arithmetic.
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