At a certain college there are twice as many

[DennaMueller]

At a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

6 to 1
3 to 2
2 to 3
1 to 5
1 to 6

I set the problem up (incorrectly):
E=2h
E=3m
Therefor 2h:3m
But the answer is 3 to 2

What am I doing wrong?

[mxs2009]

Actually, everything is correct until the last part.

We know that 2h=3m, and we want to solve for h/m

h/m = 3/2. Thus, the ratio is 3:2

[RonPurewal]

easiest way to do this problem is to PLUG IN NUMBERS, because there are no definite quantities in the problem (all you have is ratios).

it's probably easiest to pick the number of english majors first, since that quantity is in both parts of the problem.
since that number is 3 times one quantity and 2 times another quantity, you can pick 6.

the first sentence then tells you that there are 3 history majors.
the second sentence tells you that there are 2 mathematics majors.
therefore, the desired ratio is 3:2.

[DennaMueller]

Actually, everything is correct until the last part.

We know that 2h=3m, and we want to solve for h/m

h/m = 3/2. Thus, the ratio is 3:2

This makes perfect sense. Thanks!

[Ben Ku]

Glad this was helpful. You can either use a "plug in numbers" approach suggested by Ron, or to combine the ratios approach that you attempted. The key is that you look for the right thing. "Ratio of history to math" means "What is H:M?"

Let me know if there are additional questions. Thanks!

[sureng.reddy]

I got confused with "At a certain college there are twice as many english majors as history majors"
as 1 H = 2 E ; H->History and E -> English

Isn't it confusing?

[RonPurewal]

I got confused with "At a certain college there are twice as many english majors as history majors"
as 1 H = 2 E ; H->History and E -> English

Isn't it confusing?

this is an example of a math problem on which language barriers pose a non-negligible difficulty. while language barriers are clearly less of an issue than on the verbal section, they are sometimes problematic on the math section as well.

for a lifelong native speaker of english, this sentence would pose no confusion whatsoever. for a non-native speaker of the language, however, this sentence gives an important TAKEAWAY: if you see "there are twice as many X as Y", then this means the number of X is twice the number of Y.

memorize it! put it on a flash card!

[Tarigopula]

As per the given information:

E = 2H
E = 3M

This could be written as 2H = 3M

Therefore, H/M = 3/2

Ratio of H : M = 3 : 2

Could this be an alternative to the "plug-in" method?

Please let me know if I am on the right track here.

Thanks in advance!

[RonPurewal]

yes, that works. it's also posted already (it's the second post in this thread) -- please check the threads before you post, thanks.

[mtwoodford]

Hi,

I have read through the entire thread and am not convinced - please help me understand.

If 2h = E and 3m = E Why isnt this 2h/3m = 2:3 ??

Thanks for your patience and advice.

[RonPurewal]

Hi,

I have read through the entire thread and am not convinced - please help me understand.

"Not convinced" is not a helpful frame of mind here. There's no "convincing" to do here; this is the math section, on which things are either right or wrong.
On the other hand, the other part of what you wrote ("please help me understand") -- now we're talkin'.

If 2h = E and 3m = E Why isnt this 2h/3m = 2:3 ??

Here you've shown that 2h EQUALS 3m. You haven't made a ratio.

You said you read through the thread. Did you try plugging in specific numbers, as suggested?
Let E = 6.
Then 2H = 6, so H = 3. And 3M = 6, so M = 2.
What's the ratio of H to M?

Plugging in numbers is your friend!

[marketmaker87]

You could also set it up as a fraction and get the common denominator.
H:E=1:2 is the same as H/E= 1/2.
M:E=1:3 is the same as M/E= 1/3.

The lowest common denominator of these two fractions is 6.
Multiply H/E by three. 1/2*3 and get 3/6. So H/E is 3/6.
Multiply M/E by two. 1/3*2 and get 2/6. So M/E is 2/6.
Now you can compare H:M directly. 3:2.

[tim]

Thanks for sharing!