The cost per pound of tea and coffee were the same in June.

Question

The cost per pound of tea and coffee were the same in June. In July, the price of coffee shot up by 200% and that of tea dropped by 90%. If in July, a mixture containing equal quantities of tea and coffee costs $4.65 for 3lbs, how much did a pound of tea cost in July?

A. $4
B. $0.1
C. $1
D. $3
E. $1.65

A. $4
B. $0.1
C. $1
D. $3
E. $1.65

BrentGMATPrepNow · Accepted Answer

Let x = price (PER POUND) of tea in JUNE
So, Let x = price (PER POUND) of coffee in JUNE

Price of tea (PER POUND) in JULY = 0.1x (decrease by 90%).
Price of coffee (PER POUND) in JULY = 3x (increase by 200%).

In July, a mixture containing  equal  quantities of tea and coffee costs $4.65 for 3 lbs  
So, the mixture has 1.5 lbs of tea and 1.5 lbs of coffee
We can write: (cost of 1.5 lbs of tea) + (cost of 1.5 lbs of coffee) = $4.65
So: (1.5)(0.1x) + (1.5)(3x) = 4.65
Factor: 1.5(0.1x + 3x) = 4.65
Divide both sides by 1.5 to get: 0.1x + 3x = 3.1
Simplify: 3.1x = 3.1
So,  x = 1 
In other words, in JUNE the price of tea and coffee were each $ 1  per pound.

Since the price of tea in JULY = 0.1x, the price of tea = (0.1)( 1 ) = $0.1 per pound

Answer: B

Cheers,
Brent

Bunuel · Answer

Price of tea in June = price of coffee in June = $x.

Price of tea in July = 0.1x (decrease by 90%).
Price of coffee in July = 3x (increase by 200%).

In July the price of 1.5 pound of tea and 1.5 pound of coffee (equal quantities) = $4.65:
0.1x*1.5 + 3x*1.5 = 4.65;
x = 1.

Price of tea in July = 0.1x = $0.1.

Answer: B.

fameatop · Answer

Lets assume price of Coffee in June = 100x
Price of Tea in June = 100x

Price of Coffee in July = 300x (because of 200% increase in price)
Price of Tea in July = 10x (because of 90% Decrease in price)

Price of 1.5 pound of Coffee & 1.5 pound of Tea in July will be = 450x + 15x = 465x
As per question 
465x= 4.65$
x = 0.01S
So the Price of Tea in July = 10x = 10 x 0.01 = 0.1$/pound
Answer B

Bunuel · Answer

You could simply say price of tea in June = price of coffee in June = $x, instead of 100x.

ScottTargetTestPrep · Answer

We can let x = the cost per pound of tea (or coffee) in June. Thus the cost of tea in July = 0.1x and the cost of coffee in July = 3x. (Note that a price increase of 200% is a tripling of the price.) Since the price of a mixture of equal quantities of tea and coffee is $4.65 for 3 lbs, there must be 1.5 lbs of tea and 1.5 lbs of coffee. We can create the following equation:

1.5(0.1x) + 1.5(3x) = 4.65

0.15x + 4.5x = 4.65

4.65x = 4.65

x = 1

Thus, the cost of a pound of tea in July is 0.1(1) = $0.1.

Answer: B

pavkuml · Answer

How do we know one lib = 1 pound. Shouldn't it be part of the question?

Bunuel · Answer

"lb" is a common abbreviation for pound, so it's generally understood in such contexts. The question assumes this standard knowledge and doesn’t explicitly state that 1 lb = 1 pound. However, I believe a properly worded GMAT question would make this clearer.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The cost per pound of tea and coffee were the same in June.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The cost per pound of tea and coffee were the same in June.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards