A T-shirt maker has machines to make shirts with both heat-transfer

Question

A T-shirt maker has machines to make shirts with both heat-transfer and silkscreens. The heat-transfer shirts take an average of 15 minutes to make, but are sold for $10 each, while the silkscreen shirts take about 30 minutes, and can be sold for $35. If during busy times, the shirt maker earns an average of $50 an hour, what is the ratio of heat-transfer shirts sold to silkscreen shirts sold?

(A) 1:4
(B) 2:5
(C) 1:1
(D) 3:2
(E) 2:1

(A) 1:4
(B) 2:5
(C) 1:1
(D) 3:2
(E) 2:1

Yoaerez · Answer

I'm a bit stumped, would love some help:

So during busy times the maker earns $50 an hour on average:

2 HT would take 30 mins, 1 SC would take 30 mins, in total it would take 60 mins and would earn $55. ok that doesn't do much for us. busy times can be a few hours, so if busy times means 3 hours, we could do:

180 mins, would need to earn $50 an hour (150 overall)

so we could make 8 HT (120 mins, would earn 8*10 = $80), and 2 SC (60 mins, $70.) that would be 180 mins overall and $150. perfect! so the ratio would be 4:2. but that's not in the answer

so going back to the question: it says HT shirts are sold for $10, but SC shirts   can   sell for $35. does that means they could be sold for $30 as well? and then you'd have

2 HT, $20, 30 mins
1 SC, $30, 30 mins, which would make the answer 2:1.

so is this just (sort of) a trick question? I think the wording is not really similar to what you'd see on the test, but maybe i'm wrong. would love if someone could share their insights cause im probably missing something

RahulKumarSinha · Answer

Just used alligation and got the right answer in a minute.
Since, the heat-transfer shirt take 15 minutes on average to make a shirt. Therefore, in an hour it will make 4 shirts which will be sold for total of $40.
Similarly, 2 silkscreen shirts will be made & sold for a total of $70 in an hour. (We calculated money for both shirts for an hour because average is given of an hour = $50).
Thus, the number of shirts may get changed by the time, but the ratio will remain same whether in an hour or 2 or more.

Maxsmdt041197 · Answer

I still don't get it, if you say everything can change, the ratio can be everything. In your case we fullfill non of the requirements regarding 50$ per hour.

Focus799 · Answer

Heat-transfer: $40 per hour 
Silkscreens: $70 per hour 
Therefore, Avg. is $50 per hour 
Using Alligation, 
40. 70. 
 50 
2. 1
2:1 final answer

DangPham9625 · Answer

Heat: H
Silk: S
==>   =50
==> 4H=S

Gmatt1526 · Answer

Heat= H = 1/15m =$10
Silk= S = 1/30m = $35

1) 
Solve for hourly rate each product produces ($50 hourly average is the final)
H= $40/hr
S= $70/hr

2) 
Solve for proportion
* Because $50 is closer to $40 (H) than $70 (S), we know that H > S. This eliminates A, B, and C immediately.

2.a) 
3:2 = $120:$140 = $260 per proportional occurrence. This is not divisible by $50, ruling out D. It must be E.

2.b) 
2:1 = $80:$70 = $150 per proportional occurrence. This IS Divisible by $50, E is correct.

Kinshook · Answer

A T-shirt maker has machines to make shirts with both heat-transfer and silkscreens. The heat-transfer shirts take an average of 15 minutes to make, but are sold for $10 each, while the silkscreen shirts take about 30 minutes, and can be sold for $35.

If during busy times, the shirt maker earns an average of $50 an hour, what is the ratio of heat-transfer shirts sold to silkscreen shirts sold?

The money made in 1 hour by selling heat-transfer shirts = $10*60/15 = $40
The money made in 1 hour by selling silkscreen shirts = $35*60/130= $70

The ratio of heat-transfer shirts sold to silkscreen shirts sold = (70-50)/(50-40) = 20/10 = 2:1

IMO E

akhilsundar422 · Answer

I am getting 4:1 as the answer taking time constraint and revenue constraint as equations and solving them different

Su1206 · Answer

People have correctly answered E - 2:1. But in my opinion everyone has failed to give the correct reasoning.

50$ an hour is contributed by 2/3 parts of HT and 1/3 parts of SS. These are parts of 'per hour average sales' and not 'actual shirt sales'. Coincidently, the number of shirts produced per hour is also in the same ratio (4:2 or 2:1).

KarishmaB   MartyMurray   chetan2u  please correct my reasoning if its flawed. What will the answer be of HT shirts take 7.5 mins (Instead of 15) to make.

chetan2u · Answer

Earning = number of shirts × cost per shirt, so look for each case.

If it takes 7.5 minutes for one HT, a total of 8 shirts can be made and cost would be 80$, while for other shirt it is 35*2 or 70$.

In the above case average cannot be 50$ as average will be between $70 and $80..

A T-shirt maker has machines to make shirts with both heat-transfer

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A T-shirt maker has machines to make shirts with both heat-transfer