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
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 4We can write: (
8 + x)/(
20 - 2x) =
7/
4Cross 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