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If 1/3 of the total number of marbles in the three bags listed in the
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20 Aug 2016, 23:17
5
This might look like it contains hard calculations, but the thing to notice here is that the number of balls are always going to be integers.
So, 10.8% of 37 will be 4, we know 50% of x is 32 and we can keep 66.7% as 2/3rds. Once you do this, the question can be solved to arrive at ~9 quickly.
Re: If 1/3 of the total number of marbles in the three bags listed in the
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21 Aug 2016, 04:38
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3
If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?
A) 5 B) 9 C) 12 D) 23 E) 46
Total has to be multiple of 3 since 1/3rd of them are blue and 1st and 3rd bag have total 69 marbles so (69 + x)/3 is blue total hence x also must be divisible by 3
hence narrow down to B) 9 or C) 12
66.67 % is nothing but 2/3 rd (ie 33.33 * 2 ie 1/3 * 2)
so if x is 9 then blue marbles in 2nd bag is 6 (2/3rd of 9 = 6) or if x is 12 then blue marbles in 3rd bag is 8 (2/3rd of 12 = 8)
do that math : if x = 9 then total = 69 + 9 = 78 and total blue = 16 + 4 + 6 = 26 26/78 = 1/3 -----> fits (most likely that B is the ans)
cross check if x = 12 then total = 81 total blue = 28 28/81 != 1/3 hence (B)
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We are given a table with the following information:
Bag P has 37 marbles and 10.8% of those marbles are blue. So there are 0.108(37) = 3.996, or 4, blue marbles in bag P.
Bag Q has X marble and 66.7% of those marbles are blue. Recall that the fraction 2/3 is approximately 66.7%, so there are (2/3)X blue marbles in bag Q.
Bag R has 32 marbles and 50% of those marbles are blue. So, there are 0.5(32) = 16 blue marbles in bag R.
We are also given that 1/3 of the total marbles in the 3 bags are blue. Thus, we can create the following equation:
1/3(37 + X + 32) = 4 + (2/3)X + 16
Multiplying the equation by 3, we have:
37 + X + 32 = 12 + 2X + 48
X + 69 = 2X + 60
X = 9
There are 9 marbles in bag Q.
Answer: B
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here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached
\(4+16+0.67x= \frac{1}{3} (37+32+x)\)
\(20+0.67x =\frac{1}{3}x+23\)
\(20-23 = \frac{1}{3}x-\frac{67}{100}\)
\(-3 = \frac{33}{300}x\)
\(-3 = \frac{11}{100}x\)
the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong
in the next solution I converted 1/3 to decimal = 0.33%
Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33
here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached
\(4+16+0.67x= \frac{1}{3} (37+32+x)\)
\(20+0.67x =\frac{1}{3}x+23\)
\(20-23 = \frac{1}{3}x-\frac{67}{100}\)
\(-3 = \frac{33}{300}x\)
\(-3 = \frac{11}{100}x\)
the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong
in the next solution I converted 1/3 to decimal = 0.33%
Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33
here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached
\(4+16+0.67x= \frac{1}{3} (37+32+x)\)
\(20+0.67x = \frac{1}{3}x+23\)
\(20-23 = \frac{1}{3}x-\frac{67}{100}\)
\(-3 = \frac{33}{300}x\)
\(-3 = \frac{11}{100}x\)
the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong
dave13 The equation is correct. The arithmetic is off.
(EDIT As niks18 points out), check your math here:
Quote:
\(20-23 = \frac{1}{3}x-\frac{67}{100}\)
\(-3 = \frac{33}{300}x\)
Try using \(\frac{67}{100}=\frac{2}{3}\)
\(\frac{1}{3}x - \frac{2}{3}x\) = ????
Calculate again and see what you get.
Tip: use fractions with fractions and decimals with decimals. IMO fractions are easier.
Another way to think about setup and solving of the equation . . . (I do not know whether either suggestion will be easier for you - they're just possibilities)
After you replace \(.67\) with \(\frac{2}{3}\)
Change the setup and cross multiply.
(1) Setup: If blue marbles equal \(\frac{1}{3}\) of three bags' total marbles: \(\frac{Blue}{Total}=\frac{1}{3}\) \(\frac{16+4+\frac{2}{3}x}{37+32+x}=\frac{1}{3}\)
(2) Solve. Cross multiply.
Just one arithmetic mistake, in other words.
Your second solution is correct. If you use decimals (IMO, harder here!) what you calculated is correct.
here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached
\(4+16+0.67x= \frac{1}{3} (37+32+x)\)
\(20+0.67x =\frac{1}{3}x+23\)
\(20-23 = \frac{1}{3}x-\frac{67}{100}\)
\(-3 = \frac{33}{300}x\)
\(-3 = \frac{11}{100}x\)
the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong
in the next solution I converted 1/3 to decimal = 0.33%
Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33
to answer your question - How come 37+32 become 23?
\(37+32 =69\) so\(\frac{1}{3}*69 =23\) so I get \(23+0,33x\)
\(20+0.67x = 0.33x+23\)
isnt it correct ?
hi dave13 yes its correct. my mistake I got confused here. So in your method 1 the mistake is in highlighted part above. kindly check your calculation of 1/3x-67x/100. Rest is ok
If 1/3 of the total number of marbles in the three bags listed in the
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20 Sep 2018, 19:24
If we let \(x\) be the number of marbles in Bag \(Q\),
To start, the total of number of marbles in the three bags is \((37+ 32+ x) = 69 + x\) marbles.
Next, we need to find the number of blue marbles in the 3 bags. To do so, we multiply each percentage by the number of marbles in each bag (converting each percentage to decimal as needed):
The number of blue marbles present in each bag would be:
Bag P: \(0.108 \times 37 =3.996\) or \(4\) since we want the nearest whole number marbles Bag R:\(0.50 \times 32 =\)\(16\) marbles Bag Q:\(0.667(x) = 0.667x\) marbles or \(\frac{2x}{3}\) marbles (Note that 0.667 is equivalent to 2/3 in fractions)
The prompt states that \(\frac{1}{3}\) of the total marbles equals the total number of blue marbles. We can now form the equation below.
1/3 x Total Number of Marbles = Total Number of Blue Marbles
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67% (02:45) correct 
my mistake I got confused here. So in your method 1 the mistake is in highlighted part above. kindly check your calculation of 1/3x-67x/100. Rest is ok
