QR - word problem

[Mstoothlady2012]

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Can someone explain me how to solve this problem? Thanks!

A new eight-lane highway costs $7,500,000 per mile (5280 feet). If each lane measures 11 feet across, how much would it cost to pave a square mile of highway?

 

[baedero1]

is the answer 450,000,000???

 

[drgreen]

if there are 8 lanes each 11 feet across, it's 88 feet wide.
so the amount of highway that costs $7,500,000 is 5280x88 feet. since we want to know how much 5280x5280 costs we multiply $7,500,000 by 5280/88. Which gives us $450,000,000. i agree with baedero.

 

[Mstoothlady2012]

if there are 8 lanes each 11 feet across, it's 88 feet wide.
so the amount of highway that costs $7,500,000 is 5280x88 feet. since we want to know how much 5280x5280 costs we multiply $7,500,000 by 5280/88. Which gives us $450,000,000. i agree with baedero.

See that's what I don't understand why are we dividing 5280 by 88?

 

[cougarblue84]

I have a different method of thinking that gets the same answer. Maybe this helps. It costs $7,500,000 to build a highway that spans 5,280 feet by 88 ft. (8 lanes of 11 ft). To get a square mile we'd divide 5,280 by 88, which equals 60. Meaning that 60 lengths of highway equaling the distance that costs $7,500,000 could fit within 5,280 ft X 5,280 ft -- a square mile. Then multiply. $7,500,000(60) = $450,000,000

 

[cougarblue84]

Think of visually, like a square. You're trying to fill a square that is 5,280 by 5,280. Right now it's only 5,280 by 88, so you need to figure out how many "layers" so to speak of road need to be stacked on top of each other to get 5,280 by 5,280. Hope it helps.

 

[Streetwolf]

Each mile is the price given, and the area of each mile of 8 lane roadway is 5280x88 (understand so far?).

You want to know the price of a square mile. You know the price of one PIECE of a square mile which is 5280x88 in area. If that area is one piece of the big area, how many times can that one piece go into the big area of 5280x5280 (1 sq mile)?

Just do 5280x5280 / 5280x88. Simplified, this comes down to 5280/88. That's how many pieces of 1 mile length and 8 lanes across can fit into the big area. Since each of those pieces is the price listed in the problem, you take 5280/88 and multiply by the price to get your answer.

The above poster skipped the middle step when showing work.

 

[Mstoothlady2012]

Each mile is the price given, and the area of each mile of 8 lane roadway is 5280x88 (understand so far?).

You want to know the price of a square mile. You know the price of one PIECE of a square mile which is 5280x88 in area. If that area is one piece of the big area, how many times can that one piece go into the big area of 5280x5280 (1 sq mile)?

Just do 5280x5280 / 5280x88. Simplified, this comes down to 5280/88. That's how many pieces of 1 mile length and 8 lanes across can fit into the big area. Since each of those pieces is the price listed in the problem, you take 5280/88 and multiply by the price to get your answer.

The above posted skipped the middle step when showing work.

Thanks streetwolf!! I wasn't able to understand what the question was asking. You are always a saver 😍