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A municipal corporation is to paint a solid white stripe in the middle

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A municipal corporation is to paint a solid white stripe in the middle  [#permalink]

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New post 16 Oct 2018, 01:22
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  45% (medium)

Question Stats:

71% (02:44) correct 29% (02:24) wrong based on 34 sessions

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A municipal corporation is to paint a solid white stripe in the middle of a national highway. If 1 gallon of paint covers an area of a square feet of the road, how many barrels of paint will be needed to paint a stripe b inches wide on a stretch of the highway that is c miles long? (1 mile = 5,280 feet, 1 foot = 12 inches, and 1 barrel = 31.5 gallons)


(A) \(\frac{5280bc}{31.5 × 12a}\)

(B) \(\frac{5280ab}{31.5 × 12c}\)

(C) \(\frac{5280abc}{31.5 × 12}\)

(D) \(\frac{5280 × 12c}{31.5 × ab}\)

(E) \(\frac{5280 × 12a}{31.5 × bc}\)

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Re: A municipal corporation is to paint a solid white stripe in the middle  [#permalink]

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New post 16 Oct 2018, 21:00
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Bunuel wrote:
A municipal corporation is to paint a solid white stripe in the middle of a national highway. If 1 gallon of paint covers an area of a square feet of the road, how many barrels of paint will be needed to paint a stripe b inches wide on a stretch of the highway that is c miles long? (1 mile = 5,280 feet, 1 foot = 12 inches, and 1 barrel = 31.5 gallons)


(A) \(\frac{5280bc}{31.5 × 12a}\)

(B) \(\frac{5280ab}{31.5 × 12c}\)

(C) \(\frac{5280abc}{31.5 × 12}\)

(D) \(\frac{5280 × 12c}{31.5 × ab}\)

(E) \(\frac{5280 × 12a}{31.5 × bc}\)


Total area to be painted = \(\frac{b}{12} *(c *5280)\) sq ft
1 sq fit painted by = \(\frac{a}{31.5}\) barrel
Hence total barrel(s) required : \(\frac{b}{12} *(c *5280)*\frac{a}{31.5}\) = \(\frac{5280abc}{31.5 × 12}\) ...... Ans C
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Re: A municipal corporation is to paint a solid white stripe in the middle  [#permalink]

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New post 07 Feb 2019, 21:58
Bunuel wrote:
A municipal corporation is to paint a solid white stripe in the middle of a national highway. If 1 gallon of paint covers an area of a square feet of the road, how many barrels of paint will be needed to paint a stripe b inches wide on a stretch of the highway that is c miles long? (1 mile = 5,280 feet, 1 foot = 12 inches, and 1 barrel = 31.5 gallons)


(A) \(\frac{5280bc}{31.5 × 12a}\)

(B) \(\frac{5280ab}{31.5 × 12c}\)

(C) \(\frac{5280abc}{31.5 × 12}\)

(D) \(\frac{5280 × 12c}{31.5 × ab}\)

(E) \(\frac{5280 × 12a}{31.5 × bc}\)



Area = b (inches) * c (miles)

Lets convert the area into ft^2
= b/12 (ft) * 5280 * c(ft)

Now a ft^2 for 1 gallon
b/12 (ft) * 5280 * c(ft) = b/12 (ft) * 5280 * c(ft) * 1/ a (ft^2)
= bc/12 * 5280 * 1/a gallon

1 gallon = (1/31.5) barrel
bc/12 * 5280 * 1/a gallon = \(\frac{1}{31.5}\) * \(\frac{bc}{12}\) * 5280 * \(\frac{1}{a}\)

= \(\frac{5280bc}{31.5 × 12a}\)
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Re: A municipal corporation is to paint a solid white stripe in the middle   [#permalink] 07 Feb 2019, 21:58
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