Question 1151159: Blake and his children went into a bakery and where they sell donuts for $1.50 each and cookies for $0.50 each. Blake has $15 to spend and must buy no less than 12 donuts and cookies altogether. If Blake decided to buy 10 cookies, determine the maximum number of donuts that he could buy. If there are no possible solutions, submit an empty answer.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = number of cookies purchased
y = number of donuts purchased
"Blake decided to buy 10 cookies", and each cookie is $0.50, so he spends 10*0.50 = 5 dollars on those cookies. He has 15 - 5 = 10 dollars left to spend.
Blake "must buy no less than 12 donuts and cookies altogether", which means  . In other words, the total of x and y must be 12 or more.
Blake already bought 10 cookies, so x = 10 is locked in.
 Plug in x = 10
 Subtract 10 from both sides
This means Blake needs to buy 2 or more donuts.
"they sell donuts for $1.50 each", so if he buys 2 donuts, then it will cost him 2*1.50 = 3 dollars.
In general, if he buys y number of donuts at $1.50 each, then it costs him 1.50y dollars.
This amount 1.50y must be less than or equal to 10 because this is the amount of money Blake has left over (after buying those 10 cookies).
 Divide both sides by 1.50
Since y is a whole number, this means the largest y can be is y = 6.
The smallest y can be is 2 (found earlier from ), so combine  and  to get  . We can say that y is between 2 and 6 inclusive of both endpoints.
Once again, y = 6 is the largest possible y value because...
If y = 6, then 1.50*y = 1.50*6 = 9.00 dollars is spent on 6 donuts.
If y = 7, then 1.50*y = 1.50*7 = 10.50 dollars is spent on 7 donuts, but Blake only has $10 left to spend.
Answer: 6 donuts is the maximum
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