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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Tue Feb 27, 2018 8:25 am

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

The OA is B.

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%).

I stuck here. Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Feb 27, 2018 8:25 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Feb 27, 2018 9:10 am

swerve wrote: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

Let's continue where you left off:

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Mar 01, 2018 5:44 pm

swerve wrote: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

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

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