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On Monday, a class has 8 girls and 20 boys. On Tuesday, a ce
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17 Aug 2018, 17:12
17 Aug 2018, 17:12
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On Monday, a class has 8 girls and 20 boys. On Tuesday, a certain number of girls joined the class just as twice that number of boys left the class, changing the ratio of girls to boys to 7 to 4. How many boys left the class on Tuesday?
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
Re: On Monday, a class has 8 girls and 20 boys. On Tuesday, a ce
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10 Jul 2019, 09:06
10 Jul 2019, 09:06
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sandy wrote:
On Monday, a class has 8 girls and 20 boys. On Tuesday, a certain number of girls joined the class just as twice that number of boys left the class, changing the ratio of girls to boys to 7 to 4. How many boys left the class on Tuesday?
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
This question can be solved in a number of different ways - including TESTing THE ANSWERS.
We know that there are 8 girls and 20 boys to start, and a certain number of girls joined and TWICE as many boys left the class (leaving us with a ratio of 7 girls for every 4 boys). We're asked for the number of boys that LEFT the class.
To start, since the number of boys who left is TWICE the number of girls who joined, the number of boys who left MUST be an EVEN number (so we can eliminate Answers A and C immediately).
Let's TEST Answer D: 12 boys
IF... 12 boys left and 6 girls joined, we would have....
8 + 6 = 14 girls
20 - 12 = 8 boys
14:8 = 7:4
This is an exact match for what we were told, so this MUST be the answer.
Final Answer: D
#CoPy.
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Re: On Monday, a class has 8 girls and 20 boys. On Tuesday, a ce
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10 Jul 2019, 09:47
10 Jul 2019, 09:47
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sandy wrote:
On Monday, a class has 8 girls and 20 boys. On Tuesday, a certain number of girls joined the class just as twice that number of boys left the class, changing the ratio of girls to boys to 7 to 4. How many boys left the class on Tuesday?
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
(A) 5
(B) 6
(C) 11
(D) 12
(E) 18
On Monday, a class has 8 girls and 20 boys. On Tuesday, a certain number of girls joined the class just as twice that number of boys left the class...
Let x = the number of GIRLS that JOINED the class
So, 2x = the number of BOYS that LEFT the class
So, 8 + x = the number of GIRLS in the class on TUESDAY (after the x girls joined)
And, 20 - 2x = the number of BOYS in the class on TUESDAY (after the 2x boys left)
...changing the ratio of girls to boys to 7 to 4
We can write: (8 + x)/(20 - 2x) = 7/4
Cross multiply to get: (4)(8 + x) = (7)(20 - 2x)
Expand: 32 + 4x = 140 - 14x
Subtract 32 from both sides: 4x = 108 - 14x
Add 14x to both sides: 18x = 108
Solve: x = 108/18 = 6
2x = the number of BOYS that LEFT the class.
So, 2(6) BOYS left the class
In other words, 12 BOYS left the class
Answer: D
Cheers,
Brent
