Hi Zeke,

I came acroos the following two problems, the two look similair but I think the approach is slightly different. Can you help me out please?

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Lap #	This Lap	Running Total

In a certain calculus class, the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5. If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

(A) 10

(B) 12

(C) 21

(D) 28

(E) 35

So let’s break this down sentence by sentence.

OK, so what do we know from this info?
Let’s use x and y.
X = # of math majors.
Y = # of non-math majors.

So it says the ratio of math to non-math is 2:5.
Now translate that.
“# of math to non-math” = x/y
2:5 translates = 2/5

so
x          2
–   =    —-
y          5

Cross multiply and you get:
(Equation #1) 5x = 2y

Instead of (x/y), we now do ((x+2)/y)
Instead of (2/5), we now do (1/2)
x+2          1
—-    =   —–
y             2

Cross Multiply and you get:
2(x+2) = 1(y)
(Equation #2) 2x + 4 = y
Combine this with (Equaiton #1) 5x=2y from above.
Notice (Equation 1) is 2y, which is twice the total amount in (Equation #2).
So all you have to do is double (Equation #2) so it matches (Equation #1).

2x +4 = y
becomes
4x + 8 = 2y
And equation (1) is 5x = 2y.

4x + 8 = 5x
8= x
x= 8
Now plug in x into (2x+4) = y; (2(8)+4) = 20 = y

So x = 8 and y = 20.
The total number of students is # of math + # of non-math, which is x + y = 8 + 20 = 28

So that’s an answer choice D. Voila!

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