SOLUTION: Andrew, Benny and Calvin were given a box of marbles. Andrew took 1/4 of the marbles and then took another 6 marbles from the box. Benny took 1/6 of the remaining marbles and then

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Andrew, Benny and Calvin were given a box of marbles. Andrew took 1/4 of the marbles and then took another 6 marbles from the box. Benny took 1/6 of the remaining marbles and then       Log On


   

Question 1185707: Andrew, Benny and Calvin were given a box of marbles. Andrew took 1/4 of the marbles and then took another 6 marbles from the box. Benny took 1/6 of the remaining marbles and then took another 5 marbles from the box. Calvin took the remaining 45 marbles. How many marbles did Andrew take from the box?
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of marbles originally in the box.

Andrew took 1/4 of them and then 6 more. The number remaining was

x-%281%2F4%29x-6+=+%283%2F4%29x-6

Benny then took 1/6 of the remaining marbles and then another 5. The number remaining was

%28%283%2F4%29x-6%29-%281%2F6%29%28%283%2F4%29x-6%29-5

Calvin took the remaining marbles; there were 45.

%28%283%2F4%29x-6%29-%281%2F6%29%28%283%2F4%29x-6%29-5=45

Be smart about how you solve this equation. Simplifying everything at the start would make the work a lot harder. Instead, do this:

%28%283%2F4%29x-6%29-%281%2F6%29%28%283%2F4%29x-6%29-5=45

%28%283%2F4%29x-6%29-%281%2F6%29%28%283%2F4%29x-6%29=45%2B5=50

%285%2F6%29%28%283%2F4%29x-6%29=50

%283%2F4%29x-6=50%286%2F5%29=60

%283%2F4%29x=60%2B6=66

x=66%284%2F3%29=88

The original number of marbles was 88.

Andrew took 1/4 of them (22) plus another 6, for a total of 28.

ANSWER: Andrew took 28 marbles

Often this kind of problem is easier to work backwards. In this problem, there are only two steps where someone takes marbles from the box. But if there had been several people taking marbles out of the box, I think you can see the equation you would have to solve would be very messy.

So let's look at solving this one backwards.

There were 45 marbles left at the end.
Previous to that, Benny took 5 marbles, so before he did that there were 45+5=50 marbles.
Before that, Benny took 1/6 of the marbles, which means the 50 marbles were 5/6 of what there were before he took 1/6. That means the number of marbles before Benny took any was 50(6/5)=60.
Before that, Andrew took 6 marbles, so there were 60+6=66 marbles before he did that.
And before that, Andrew took 1/4 of the marbles, so the 66 marbles were 3/4 of what was originally in the box. So the original number of marbles was 66(4/3)=88.

So we of course end up with the same original number of marbles, and so again our answer to the problem is that Andrew took 22+6=28 marbles.

You should also note that the calculations we did in solving the problem backwards are EXACTLY the same as the steps we used in solving the problem using an equation....

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Andrew, Benny and Calvin were given a box of marbles. Andrew took 1/4 of the marbles and then took another 6 marbles from the box. Benny took 1/6 of the remaining marbles and then took another 5 marbles from the box. Calvin took the remaining 45 marbles. How many marbles did Andrew take from the box?
Let original number of marbles be M
After Andrew took 1%2F4 of the marbles, and another 6 marbles, matrix%281%2C3%2C+%283%2F4%29M+-+6%2C+or%2C+3M%2F4+-+6%29 remained
After Benny took 1%2F6 of the remainder, and another 5 marbles,  remained
As 45 marbles remained in the end, we get: matrix%281%2C3%2C+5M%2F8+-+10%2C+%22=%22%2C+45%29
5M - 80 = 360 ------ Multiplying by LCD, 8
5M = 440
Original number of marbles, or matrix%281%2C5%2C+M%2C+%22=%22%2C+440%2F5%2C+%22=%22%2C+88%29

Amount Andrew took: