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A carpet is y yards long and f feet wide. How many dollars will it cos

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Math Expert

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Posts: 58449

A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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18 Mar 2018, 23:55

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Difficulty:

85% (hard)

Question Stats:

50% (01:28) correct

50% (01:22) wrong

based on 158 sessions

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A carpet is y yards long and f feet wide. How many dollars will it cost if the carpet sells for x cents per square foot? (1 yard = 3 feet)

(A) xyf

(B) 3xyf

(C) xyf/3

(D) 0.03yf/x

(E) 0.03xyf

Spoiler: OA

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Math Expert

Joined: 02 Sep 2009

Posts: 58449

Re: A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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18 Mar 2018, 23:57

Bunuel wrote:

A carpet is y yards long and f feet wide. How many dollars will it cost if the carpet sells for x cents per square foot? (1 yard = 3 feet)

(A) xyf

(B) 3xyf

(C) xyf/3

(D) 0.03yf/x

(E) 0.03xyf

Check other Conversion problems to practice in Special Questions Directory.
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Re: A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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19 Mar 2018, 00:08

Bunuel wrote:

A carpet is y yards long and f feet wide. How many dollars will it cost if the carpet sells for x cents per square foot? (1 yard = 3 feet)

(A) xyf

(B) 3xyf

(C) xyf/3

(D) 0.03yf/x

(E) 0.03xyf

IMO E.

This is a conversion problem and the conversion factor is given - 1 yard is equal to 3 feet.

length of carpet = y yards = 3y feet.
width = f feet.
area = length * wight = 3yf square feet.

rate of carpet = x cents per square feet.

cost ( in cents ) = 3xyf this is the trap option! We are asked cost in dollars not cents... so we need to apply the implicit conversion of 100 cents a dollar

cost ( in dollars ) = 3xyf / 100 or 0.03xyf.

Hence Option E.

Best,
Gladi
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A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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19 Mar 2018, 01:13

Bunuel wrote:

A carpet is y yards long and f feet wide. How many dollars will it cost if the carpet sells for x cents per square foot? (1 yard = 3 feet)

(A) xyf

(B) 3xyf

(C) xyf/3

(D) 0.03yf/x

(E) 0.03xyf

To make things easier, we'll pick easy numbers for x, y and f.
This is an Alternative approach.

Say y = 1 yard = 3 feet, f = 1 foot and x = 100 cents = 1 dollar per square foot.
Then our total cost in feet per dollar is 3*1*1 = 3 dollars.
Looking at our answer,
A. 1*1*100 = 100 NO.
B. 3*100*1*1 = 300 NO.
C. 100*1*1/3 = 100/3 NO.
D. 0.03*1*1/100 = 0.03/100 NO.
E. 0.03*100*1*1 = 3.

(E) is our answer.
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Re: A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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20 Mar 2018, 16:59

Bunuel wrote:

A carpet is y yards long and f feet wide. How many dollars will it cost if the carpet sells for x cents per square foot? (1 yard = 3 feet)

(A) xyf

(B) 3xyf

(C) xyf/3

(D) 0.03yf/x

(E) 0.03xyf

Since y yards = 3y feet, the area of the carpet is 3y x f = 3yf square feet.

Since the carpet sells for x cents, or x/100 dollars, per square foot, the carpet will cost (3yf)(x/100) = 3xyf/100 = 0.03xyf dollars.

Answer: E
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Re: A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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22 Mar 2018, 00:08

y yard = 3y ft

3y * f* x = 3yfx cents

100 cents = 1 dollar

3yfx / 100 = 0.03yfx

answer: E

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Re: A carpet is y yards long and f feet wide. How many dollars will it cos [#permalink]

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20 Apr 2018, 03:08

The two traps in the question

a) length and width are in different units.
b) Cost required is in dollars and not cents.

Use the formula for area and the cost/area to calculate the total cost.

Option E it is
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