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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio
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14 Nov 2016, 07:44
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changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
A. 8 B. 9 C. 10 D. 11 E. 12
The ratio of boys to girls in Class A is 3 to 4. Let B = number of boys in class A Let G = number of girls in class A We get: B/G = 3/4 Cross multiply to get: 4B = 3G
Class A has one more boy and two more girls than class B So B - 1 = number of boys in class B So G - 2 = number of girls in class B
The ratio of boys to girls in Class B is 4 to 5 We get: (B - 1)/(G - 2) = 4/5 Cross multiply to get: 5(B - 1) = 4(G - 2) Expand: 5B - 5 = 4G - 8
So, we now have the following system to solve for G: 4B = 3G 5B - 5 = 4G - 8
Take 4B = 3G and solve for B to get: B = 3G/4
Take 5B - 5 = 4G - 8 and replace B with 3G/4 We get: 5(3G/4) - 5 = 4G - 8 Expand: 15G/4 - 5 = 4G - 8 Multiply both sides by 4 to get: 15G - 20 = 16G - 32 Solve to get: G = 12 Answer:
The ratio of boys to girls in Class A is 3 to 4. The ratio
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24 May 2017, 07:35
Here's the simplest approach I found. First look at the new ratio 17:22 recognize that 17 is a prime number. There're only so many ways to arrive at 17.
3:4 Girls = 17 4:5 boys = 22
3x + 4y = 17--> 3*(3) = 4*(2) = 17. Now lets try. 4*(3) + 5*(2) = 22. So that adds up.
Re: The ratio of boys to girls in Class A is 3 to 4. The ratio
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04 Apr 2019, 18:16
changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
A. 8 B. 9 C. 10 D. 11 E. 12
We can create the ratios:
Class A:
Boys : girls = 3x : 4x
Class B:
Boys : girls = 4y : 5y
Combining, we have:
(3x + 4y)/(4x + 5y) = 17/22
22(3x + 4y) = 17(4x + 5y)
66x + 88y = 68x + 85y
3y = 2x
Also, we are given that class A has one more boy and two more girls than class B. So we have:
3x = 4y + 1 and 4x = 5y + 2
Since 3y = 2x, we know that 6y = 4x, and therefore we have:
6y = 5y + 2
y = 2
Since class A has 4x girls and 4x = 5y + 2, we have 5(2) + 2 = 12 girls in class A.