SOLUTION: Suppose you are shopping at the fruit market. You want to spend no more than $12.00 on apples and bananas. Bananas cost $2 per bunch, and apples cost $4 per bag. Find 3 possible co

Algebra ->  Inequalities -> SOLUTION: Suppose you are shopping at the fruit market. You want to spend no more than $12.00 on apples and bananas. Bananas cost $2 per bunch, and apples cost $4 per bag. Find 3 possible co      Log On


   

Question 198352: Suppose you are shopping at the fruit market. You want to spend no more than $12.00 on apples and bananas. Bananas cost $2 per bunch, and apples cost $4 per bag. Find 3 possible combinations of bananas and apples that you can buy. Write each combination as an ordered pair. Let x be the number of banana bunches, and let y be the number of apple bags.
Please help me solve this problem.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of banana bunches and y=# of apple bags

Since "Bananas cost $2 per bunch, and apples cost $4 per bag" and "You want to spend no more than $12.00 on apples and bananas", this means that we have the inequality

2x%2B4y%3C=12


2%28x%2B2y%29%3C=12 Factor out the GCF 2 on the left side


x%2B2y%3C=6 Divide both sides by 2.


x%3C=6-2y Subtract 2y from both sides.


Since "x" is the number of banana bunches, this means that "x" is a whole number that is NOT negative. So x%3E=0. This means that 6-2y%3E=0 also.


6-2y%3E=0 Start with the given inequality.


6%3E=2y Add 2y to both sides.


2y%3C=6 Rearrange the inequality


y%3C=3 Divide both sides by 2.


So you can buy at most 3 apple bags. Note: if you bought only apples, then you could only buy 12%2F4=3 bags.


Since you can buy at most 3 apple bags, this means that the possible y values are: 0, 1, 2, and 3

Plug these values back into the equation x=6-2y to get:

y=0 ---> x=6-2%280%29 ---> x=6. So one ordered pair is (6,0). In other words, in this case, you buy 6 banana bunches and no apple bags.


y=1 ---> x=6-2%281%29 ---> x=4. So one ordered pair is (4,1). In other words, in this case, you buy 4 banana bunches and 1 apple bag.


y=2 ---> x=6-2%282%29 ---> x=2. So one ordered pair is (2,2). In other words, in this case, you buy 2 banana bunches and 2 apple bags.


y=3 ---> x=6-2%283%29 ---> x=0. So one ordered pair is (3,0). In other words, in this case, you buy no banana bunches and 3 apple bags.


and so on...


Here are ALL the possible ordered pairs: (0,0), (0,1), (0,2), (0,3), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0), (4,1), (5,0), (6,0)


Take note that you are allowed to spend under $12. So the first ordered pair (0,0) means you did not buy anything.