Stuck on this Geometry problem?

Question

to have wall-to-wall carpeting for two rooms. One room is 9 ft by 12 ft and the other room is 12 ft by 15 ft. How much will it cost him if the carpet costs $10.50 per square yard?

I know we would multiply 9x12 and 12x15 but since its square yardage what do we divide it by?

Answer 1

(9)(12) + (12)(15) = 108 + 180 = 288 square feet

288 square feet = 288 feet*feet =
288*(1 yard/3 feet)*(1 yard/3 feet) = 32 square yards

32 square yards * $10.50/square yard =

32*10.5 = $336

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Edit: Forgot to check my units first time through, rhsaunders and james k were right.

Answer 2

There are two different ways you could go about this. You could first just convert all of the feet into yards (3 ft = 1 yd). So this becomes one 3 yard by 4 yard room, and one 4 yard by 5 yard room. Then multiplying the pairs of numbers together gives you the area of each room in square yards.

Alternatively, you could do all the calculations in feet to give you square feet, then convert square feet to square yards. If 3 feet is in 1 yard, then you square both to get square feet per square yard. So 3^2 square feet (9 ft^3) are in 1 yd^2. (This makes sense if you think about it: if you had a square piece of rug that measured 1 yard x 1 yard, and drew horizontal and vertical lines to split it up into 1 ft x 1 ft squares, you'd have 9 of them.) So after finding out the answer in square feet you could divide by 9 to get square yards.

Answer 3

first off, figure out the answer in sq ft. if you multiply the length times the width of both rooms (to get the area of each room) and then add the two sums up (to get a total area) you should end up with 288 sq ft total for the two rooms. now you have to convert the answer to sq yards. to do this 288 ft^2*[(1 yard/3 feet)^2] (make sure you square both the numerator, to get sq ft, and the denominator to get sq yds) and you should basically end up dividing the 288 ft^2 by 9 (there is 9 sq ft in a sq yd) to get 32 square yds. mult 32 sq yds * 10.50 per square yd and you should get $336.

Answer 4

The dimensions of the first room (in yards) is 3 yard by 4 yard; the dimensions of the second room, in yard, is 4 by 5.

Therefore, the area of the first room is 12 sq yards and the second is 20 sq yards: total area is therefore 32 sq yards. Finally, multiply this by 10.50 to get $336.

Answer 5

Since one yard is three feet, one square yard is nine square feet. So divide by nine.