A waitress's income consist of her salary and tips. During

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AAPL: Moderator; Posts: 2710; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Jan 29, 2019 3:53 am

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A waitress's consist of her salary and tips. During one week, her tips were 5/4 of her salary. What fraction of her income for the week came from tips?

A. 1/9
B. 1/6
C. 1/3
D. 4/9
E. 5/9

OA E

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Source: Beat The GMAT — Problem Solving | Tue Jan 29, 2019 3:53 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Jan 29, 2019 4:07 am

AAPL wrote:GMAT Prep

A waitress's income consist of her salary and tips. During one week, her tips were 5/4 of her salary. What fraction of her income for the week came from tips?

A. 1/9
B. 1/6
C. 1/3
D. 4/9
E. 5/9

$$? = {{{\rm{tips}}} \over {{\rm{salary}}\,\,{\rm{and}}\,\,{\rm{tips}}}} = {{{5 \over 4}\left( {{\rm{salary}}} \right)} \over {\left( {{4 \over 4} + {5 \over 4}} \right)\left( {{\rm{salary}}} \right)}} = {5 \over 9}$$

Alternate way (exploring a particular case):

$${\rm{salary}} = 4\,\,\, \Rightarrow \,\,\,{\rm{tips}} = 5\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = {5 \over {4 + 5}} = {5 \over 9}$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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

by Brent@GMATPrepNow » Tue Jan 29, 2019 5:42 am

AAPL wrote:GMAT Prep

A waitress's income consist of her salary and tips. During one week, her tips were 5/4 of her salary. What fraction of her income for the week came from tips?

A. 1/9
B. 1/6
C. 1/3
D. 4/9
E. 5/9

APPROACH #1 - start with a convenient value of the server's salary
Let's say her salary is $4

GIVEN: her tips were 5/4 of her salary
5/4 of $4 = $5
So, her tip total was $5

What fraction of her income for the week came from tips?
Income = salary + tips
= $4 + $5 = $9
Fraction = $5 /$9

Answer: E
-------------------------
APPROACH #2 - Algebraic

Let x = her salary (in dollars)

GIVEN: her tips were 5/4 of her salary
So, tips = 5/4 of x
= 5x/4
So, her tip total was 5x/4 dollars

What fraction of her income for the week came from tips?
Income = salary + tips
= x + 5x/4
= 4x/4 + 5x/4
= 9x/4
Fraction = (5x/4) /9x/4
= (5x/4)(4/9x)
= 5/4

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jan 31, 2019 5:36 pm

AAPL wrote:GMAT Prep

A waitress's consist of her salary and tips. During one week, her tips were 5/4 of her salary. What fraction of her income for the week came from tips?

A. 1/9
B. 1/6
C. 1/3
D. 4/9
E. 5/9

OA E

We can let x = her salary for the week and so her tips = 5x/4.

To determine the fraction that her tips represent out of her total income, we use: fraction = tips/total income. Thus, her tips are (5x/4)/(x + 5x/4) = (5x/4)/(4x/4 + 5x/4) = (5x/4)/(9x/4) = 5/9 of her income.

Alternate Solution:

Since her tips are 5/4 of her salary, she made more from the tips than her salary. Thus, the fraction of her income for the week that came from the tips must be greater than 1/2. The only answer choice that is greater than 1/2 is E.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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