Brian purchased a bouquet of 40 flowers for his mother for

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Oct 18, 2018 4:40 am

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Veritas Prep

Brian purchased a bouquet of 40 flowers for his mother for her birthday. If roses cost $1.50 and tulips cost $1.00, and he spent $48 in total buying only those two types of flowers, how many tulips were in the bouquet?

A. 12
B. 16
C. 20
D. 24
E. 28

OA D

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Source: Beat The GMAT — Problem Solving | Thu Oct 18, 2018 4:40 am

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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 » Thu Oct 18, 2018 4:53 am

AAPL wrote:Veritas Prep

Brian purchased a bouquet of 40 flowers for his mother for her birthday. If roses cost $1.50 and tulips cost $1.00, and he spent $48 in total buying only those two types of flowers, how many tulips were in the bouquet?

A. 12
B. 16
C. 20
D. 24
E. 28

OA D

We can solve this question using either 1 variable or 2 variables.
Here's an approach that involves 1 variable:

Let t = # of tulips in bouquet
So. 40 - t = # of roses in bouquet [since the total number of flowers is 40, the number of roses must be 40-t]

So, ($1.00)(t) = the total COST of all t tulips
And ($1.50)(40 - t) = the total COST of all 40-t roses

We're told the bouquet costs $48.
So, we can write: ($1.00)(t) + ($1.50)(40 - t) = 48
Expand: t + 60 - 1.5t = 48
Simplify: 60 - 0.5t = 48
Subtract 60 from both sides: -0.5t = -12
Solve: t = 24

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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

by fskilnik@GMATH » Thu Oct 18, 2018 5:25 am

AAPL wrote:Veritas Prep

Brian purchased a bouquet of 40 flowers for his mother for her birthday. If roses cost $1.50 and tulips cost $1.00, and he spent $48 in total buying only those two types of flowers, how many tulips were in the bouquet?

A. 12
B. 16
C. 20
D. 24
E. 28

$$40\,\,\left\{ \matrix{
\,\,T\,\, = \,\,? \hfill \cr
\,R = 40 - T \hfill \cr} \right.$$
$$\left[ \$ \right]\,\,\,\,\left( {40 - T} \right) \cdot \frac{3}{2} + T \cdot 1 = 48\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,60 - \frac{1}{2}T = 48\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\frac{1}{2}T = 12\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( D \right)$$

This solution follows 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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Oct 18, 2018 6:06 am

AAPL wrote:Veritas Prep

Brian purchased a bouquet of 40 flowers for his mother for her birthday. If roses cost $1.50 and tulips cost $1.00, and he spent $48 in total buying only those two types of flowers, how many tulips were in the bouquet?

A. 12
B. 16
C. 20
D. 24
E. 28

We can PLUG IN THE ANSWERS, which represent the number of tulips.
When the correct answer is plugged in, the total cost = $48.

D: 24 tulips, implying 16 roses, for a total of 40 flowers
Since each of the 24 tulips costs $1, and each of the 16 roses costs $1.50, we get:
Total cost = (24*1) + (16*1.5) = 24 + 24 = 48.
Success!

The correct answer is D.

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by Scott@TargetTestPrep » Fri Oct 19, 2018 2:24 pm

AAPL wrote:Veritas Prep

Brian purchased a bouquet of 40 flowers for his mother for her birthday. If roses cost $1.50 and tulips cost $1.00, and he spent $48 in total buying only those two types of flowers, how many tulips were in the bouquet?

A. 12
B. 16
C. 20
D. 24
E. 28

We can let the number of tulips = t and the number of roses = r and create the following equations:

t + r = 40

t = 40 - r

and

1.5r + t = 48

Thus:

1.5r + 40 - r = 48

0.5r = 8

r = 16

So, t = 40 - 16 = 24.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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by [email protected] » Sat Oct 20, 2018 11:24 am

Hi All,

We're told that Brian purchased a bouquet of 40 flowers for his mother for her birthday; roses cost $1.50 each and tulips cost $1.00 each , and he spent $48 in total buying only those two types of flowers. We're asked for the number of tulips that he bought. This question can be solved in a variety of ways; it's essentially a Weighted Average question, so you can use a little logic and a bit of math to find the correct answer.

IF... we had an EQUAL number of roses and tulips, then the AVERAGE cost of the flowers would be $1.25 and the TOTAL cost would be (40)($1.25) = $50.

We're told that the total cost was $48 though - and that's a bit less than $50 - so there are just slightly more of the $1 flowers (the tulips) than there are of the roses. Thus, a little more than half of the 40 flowers would be tulips. There's only one answer that's a little more than 20...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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