Question 1042340: Please help me solve this problem:
Andrew and Bobby both opened restaurants at the same time. Andrew reported that on the first week after opening his restaurant, he had a profit of $500, and every week after that, his profit continually increased by 12%. Bobby reported that on the first week after opening his restaurant, he had a profit of $600, and every week after that, his profit continually increased by 8%.
Use the information given above to determine how long Bobby will have a higher profit than Andrew.
The first week Andrew will have a higher profit than Bobby will occur ____
weeks after he opens his restaurant.
The first week when Andrew's profit is higher than Bobby's, Bobby starts an advertising campaign that makes his weekly profit begin to increase by 15%. Taking this change into account, what will Bobby's weekly profit be 14 weeks after opening his restaurant? ___
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Linear_Equations_And_Systems_Word_Problems/1042340 (2016-07-26 13:12:22): Please help me solve this problem:
Andrew and Bobby both opened restaurants at the same time. Andrew reported that on the first week after opening his restaurant, he had a profit of $500, and every week after that, his profit continually increased by 12%.
1st:: 500
2nd:: 500(1.12)
3rd:: 500(1.12)^2
nth:: 500(1.12)^(n-1)
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Bobby reported that on the first week after opening his restaurant, he had a profit of $600, and every week after that, his profit continually
increased by 8%.
nth:: 600(1.08)^(n-1)
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Use the information given above to determine how long Bobby will have a higher profit than Andrew.
Solve:
600(1.08)^(n-1) > 500(1.12)^(n-1)
(1.08)^(n-1) > (5/6)(1.12)^(n-1)
[1.12/1.08]^(n-1) < 6/5
1.029^(n-1) < 6/5
(n-1)< log(6/5)/log(1.029)
n-1 < 6.377
n < 7.377
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Ans:: For 7 weeks Bobby will be higher than Andrew
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The first week Andrew will have a higher profit than Bobby will occur 8 ____
weeks after he opens his restaurant.
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The first week when Andrew's profit is higher than Bobby's, Bobby starts an advertising campaign that makes his weekly profit begin to increase by 15%. Taking this change into account, what will Bobby's weekly profit be 14 weeks after opening his restaurant? ___
Comment:: I'll leave that change to you.
Cheers,
Stan H.
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