A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?
A. 14
B. 28
C. 42
D. 56
E. 70
The OA is B.
I'm confused by this PS question.
If the initial ratio is 4/10, then (4+2)/10=2/4.
I stuck here. Experts, any suggestion? Thanks in advance.
A physics class has majors and non-majors in a ratio of...
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The ratio of the number of physics majors to non-physics majors is 3 to 5LUANDATO wrote:A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?
A. 14
B. 28
C. 42
D. 56
E. 70
Let P = number of Physics majors
Let N = number of Non-physics majors
So, we get: P/N = 3/5
Cross multiply to get: 5P = 3N
Rearrange to get: 5P - 3N = 0
If two of the physics majors were to change their major to biology, the new ratio of physics majors to non-physics majors would be 1 to 2
This means that P - 2 = the NEW number of Physics majors
And N + 2 = the NEW number of Non-physics majors
So, we get: (P - 2)/(N + 2) = 1/2
Cross multiply to get: 2(P - 2) = 1(N + 2)
Expand: 2P - 4 = N + 2
Rearrange to get: 2P - N = 6
We now have two equations:
5P - 3N = 0
2P - N = 6
Multiply BOTTOM equation by 3 to get:
5P - 3N = 0
6P - 3N = 18
Subtract top equation from bottom to get: P = 18
Answer: B
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We can PLUG IN THE ANSWERS, which present the total number of people in the class.LUANDATO wrote:A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?
A. 14
B. 28
C. 42
D. 56
E. 70
Let P = physics majors and N = non-physics majors.
When the correct answer is plugged in, adding 2 physics majors will yield the following ratio:
(New P)/N = 2/4 = 1/2.
B: total = 28
In this case:
Since P:N = 4:10 = 8:20, P=8 and N=20, with the result that the total number of students = 8+20 = 28.
After 2 physics majors are added -- increasing the value of P from 8 to 10 -- we get:
(new P)/N = 10/20 = 1/2.
Success!
The correct answer is B.
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We see that the ratio of majors to non-majors = 4x : 10x. When two more majors were to be added to the class, the ratio would then be 2 to 4, and thus:LUANDATO wrote:A physics class has majors and non-majors in a ratio of 4 to 10. If two more majors were to be added to the class, the ratio would then be 2 to 4. How many people are in the class?
A. 14
B. 28
C. 42
D. 56
E. 70
(4x + 2)/10x = 2/4
4(4x + 2) = 20x
16x + 8 = 20x
8 = 4x
2 = x
So there are 4(2) + 10(2) = 28 people in the class.
Answer: B
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