Question 1013818: A school bought red & blue pens in separate boxes.all boxes of red pens held the same number of pens.each box of blue pens held 70. The school bought 300 pens in total.which of these could not be the number of red pens in a box?
A) 32
B)36
C)45
D)46
How we have to solve this one please help me
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! can't be 36.
here's why:
there are 70 blue pens in a box.
the number of blue pens will therefore be a multiple of 70.
they can be either 70, 140, 210, or 280.
if the number of blue pens is 70, then the number of red pens has to be 230.
if the number of blue pens is 140, then the number of red pens has to be 160.
if the number of blue pens is 210, then the number of red pens has to be 90.
if the number of blue pens is 280, then the number of red pens has to be 20.
your selections for the number of red pens is:
A)32
B)36
C)45
D)46
the number of red pens in each box of red pens has to be the same.
therefore, the total number of red pens has to be a multiple of at least one of the possible number of total red pens.
32 * 5 = 160 so 32 pens in a red box is possible.
45 * 2 = 90 so 45 pens in a red box is possible.
46 * 5 = 230 so 46 pens in a red box is possible.
36 does not divide evenly into any of the possible total number of red pens so 36 is the one that is not possible.
your total possible combinations are:
1 box of black pens plus 5 boxes of red pens with 46 pens in a box.
you get 70 + 5 * 46 = 670 + 230 = 300
3 boxes of black pens plus 2 boxes of red pens with 45 pens in a box.
you get 210 + 90 = 300.
2 boxes of black pens plus 5 boxes of red pens with 32 pens in a box.
you get 140 + 160 = 300.
there are no combinations where the number of red pens in a box is 36.
230 / 36 = 6.38...
160 / 36 = 4.44...
90 / 36 = 2.5
20 / 36 = .55...
36 is your solution.
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