Jam Jars Math Brainteaser (Beginning Algebra Level)

[Otis]

Joey spends a certain sum of money to buy a number of jars of jam. If he had been able to buy nine more jars for the same amount of money, the jars would have each cost $3 less. If he had purchased three jars fewer for the same amount of money, the jars would have each cost $3 more. How many jars did he buy?

?

[imath]\;[/imath]

 

[lookagain]

Something seems amiss with this problem:

Spoiler

Let M = money spent per jar originally (bought)
Let x = the number of jars originally

Then M*x, or Mx, equals the certain sum of money spent on the number of jars

Mx = (x + 9)(M - 3)
Mx = (x - 3)(M + 3)
---------------------

Mx = Mx + 9M - 3x - 27
Mx = Mx - 3M + 3x - 27
--------------------------

9M - 3x - 27 = 0
-3M + 3x - 27 = 0
--------------------

3M - x - 9 = 0
-3M + 3x - 27 = 0
--------------------
2x - 36 = 0

2x = 36

x = 18 . . . . . . . . supposed answer

Substituting back, M = 9.

Mx (the certain sum of money) = (9)(18) = 162

Checking:

162 = (18 + 9)(9 - 3) = (27)(6) = 162 . . . . True.

162 = (18 - 3)(9 + 3) = (15)(12) = 180 . . . . False.

?

 

[Dr.Peterson]

Spoiler

Mx = (x + 9)(M - 3)
Mx = (x - 3)(M + 3)

Mx = Mx + 9M - 3x - 27
Mx = Mx - 3M + 3x - 27

Check that one (marked) multiplication. I got correct answers by almost the same work.

 

[lookagain]

Check that one (marked) multiplication. I got correct answers by almost the same work.

Thank you. You showed me my arithmetic was amiss. And then my
other errors played off of that.