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

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
A municipal corporation is to paint a solid white stripe in the middle  [#permalink]

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16 Oct 2018, 01:22
00:00

Difficulty:

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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16 Oct 2018, 21:00
1
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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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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