Lorraine and Colleen are trading stickers for buttons. Each large sticker is worth a large button or three small buttons. A small sticker is worth one small button. A large button is worth three small stickers. Lorraine starts with 30 small stickers and 40 large stickers. She trades 90% of her small stickers for large buttons. She trades 50% of her large stickers for large buttons and trades the rest of them for small buttons. How many buttons does she have by the end?
Answer: Lorraine has a total of 69 buttons by the end.
Step-by-step solution
Step 1: Calculate Small Stickers Traded
Lorraine starts with 30 small stickers and trades 90% of them. To find the number of small stickers traded, we multiply the total number of small stickers by the given percentage.
Step 2: Convert Small Stickers to Large Buttons
Since 1 large button is worth 3 small stickers, we can convert the traded small stickers into large buttons by dividing the number of small stickers by 3.
Step 3: Calculate Large Stickers Traded for Large Buttons
Lorraine has 40 large stickers and trades 50% of them for large buttons. We calculate this number to determine how many large stickers were converted into large buttons.
Step 4: Convert Large Stickers to Large Buttons
Each large sticker is worth one large button. Therefore, the number of large buttons obtained from these large stickers is equal to the number of large stickers traded for them.
Step 5: Calculate Large Stickers Traded for Small Buttons
After trading 50% of her large stickers for large buttons, the remaining large stickers are traded for small buttons. We find this amount by subtracting the stickers used for large buttons from the total large stickers.
Step 6: Convert Large Stickers to Small Buttons
Each large sticker is worth three small buttons. We multiply the number of large stickers traded for small buttons by 3 to find the total number of small buttons received.
Step 7: Calculate Total Buttons
Finally, we sum the total number of large buttons and the total number of small buttons obtained from all trades to find the grand total of buttons Lorraine has.
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