SOLUTION: Bob wants to buy 5 packages of batteries. He has $25 to spend. Each regular package of batteries costs $4.25 and each alkaline package of batteries costs $5.50. How many packages o

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Bob wants to buy 5 packages of batteries. He has $25 to spend. Each regular package of batteries costs $4.25 and each alkaline package of batteries costs $5.50. How many packages o      Log On

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Question 1154156: Bob wants to buy 5 packages of batteries. He has $25 to spend. Each regular package of batteries costs $4.25 and each alkaline package of batteries costs $5.50. How many packages of each type of battery can he buy? *
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of pkgs reg batteries
+5+-+x+ = number of pkgs alkaline batteries
----------------------------------------------------
+4.25x+%2B+%28+5+-+x+%29%2A5.5+=+25+
+4.25x+%2B+27.5+-+5.5x+=+25+%7D%7D%0D%0A%7B%7B%7B+1.25x+=+2.5+
+x+=+2+
and
+5+-+2+=+3+
------------------
2 pks reg batts
3 pkgs alk batts
-------------------
check:
+4.25x+%2B+%28+5+-+x+%29%2A5.5+=+25+
+4.25%2A2+%2B+3%2A5.5+=+25+
+8.5+%2B+16.5+=+25+
+25+=+25+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note the problem only says he has $25 TO SPEND; it does not say he has to spend the whole $25. So he can buy

(a) 5 packages of regular batteries: 5($4.25) = $21.25; or
(b) 4 of regular batteries and 1 of alkaline: 4($4.25)+1($5.50) = $22.50; or
(c) 3 of regular and 2 of alkaline: 3($4.25)+2($5.50) = $23.75; or
(d) 2 of regular and 3 of alkaline: 2($4.25)+3($5.50) = $25

Obviously if he is supposed to spend the whole $25 the last option is the right one....

Also note that if he is supposed to spend the whole $25, there are many ways to get to the answer without formal algebra.

You could, of course, list all the possible combinations of 5 packages and find the one that costs a total of $25.

I solved this mentally three different ways before writing my response. My first solution went like this:

(1) with prices of $4.25 and $5.50, and a total cost of $25.00, the number of packages at $4.25 can't be an odd number;
(2) so the number of packages of regular batteries must be either 2 or 4;
(3) and trying those two possibilities shows the correct answer is 2 packages of regular an 3 of alkaline.