arithmetics

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hello can someone help me understand these questions? It's for a test that has arithmetic questions on it and Im trying to study them but I cant do that unless I actually know how to do them.

#5 A carpenter needs 4 boards, each 2 feet 9 inches long. If wood is sold only by the foot, how many feet must he buy? the answer is 11 but how do you get 11?

#7On a blueprint in which 2 inches represent 5 feet, the length of a room mesure 7 1/2 inches. The actual length of the room is? 18 3/4

#8Durning a 25% sale, an article sells for \$375, what was the original price of this article?

#10A piece of wood 35 feet 6 inches long was used to make 4 shelves of equal lenth. The lenth of each shelf was? 8 feet 10 1/2 inches

#21 A crate containing a tool that weighs 12 pounds. If the tool weighs 9 pounds, 9 ounces, how much does the crate weigh? 2 pounds,7 ounces

#22The area of a room mesuring 12 feet by 15 feet is? 20 square yards.

#28If 1/2 cup of spinach contains 80 calories and the same amount of peas contains 300 calories, how many cups of spinach have the same caloric content as a 2/3 cup of peas?
2 1/

#5 A carpenter needs 4 boards, each 2 feet 9 inches long. If wood is sold only by the foot, how many feet must he buy? the answer is 11 but how do you get 11?

You need to multiply 4 times 2 3/4 to find the total amount of board feet the carpenter needs. (9 inches is 9/12 or 3/4 of a foot.) Do you get 11 by doing this?

#7On a blueprint in which 2 inches represent 5 feet, the length of a room mesure 7 1/2 inches. The actual length of the room is? 18 3/4

The easiest way to do this problem is to set up a ratio. Let x equal the blueprint measure of the room.

Five feet is to two inches as 18 3/4 feet is to x inches
2 / 5 x 7 1/2 / x

Cross multiply -- 2x = 5(7 1/2)

#8Durning a 25% sale, an article sells for \$375, what was the original price of this article?

You can set up a simple equation, with x = the original price.

.75 x = 375

_________________________

#5. to get the 11 they just multiplied 4 by 2.75.

(2 feet 0 inches = 2 feet + 9/12 feet
9/12=.75
so 2 feet 9 inches = 2/75 feet)

This is an unrealistic answer since it ignores the loss you will have when you cut the 11 feet into the 4 pieces.

#7 set up a ratio

2 in = 5 feet
7.5 in = x feet
2/7.5 = 5/x
2x = 7.5 x 5
2x=37.5
x=18.75
so the room is 18 3/4 feet

#8 the \$375 represents 75% of the original price.
so or. price = 375/.75
= 500 (test it by taking 1/4 away from 500)

#10 35feet 6 inches = 35.5 feet
so divide 35.5 by 4 to get their 8.875 feet

(.875 = 7/8, so 3/8 of a foot
= 7/8 x 12
= 10.5 inches, so 10 1/2 inches)

((Man, this working in non-metric is for the birds!!!!, not used to it anymore))

#21
take 12 lbs - 9 lbs, 9 oz
= 12 - 9 9/16
= 192/16 - 153/16
= 39/16
= 2 7/16 lbs
= 2 lbs and 7 ounces

gee, this would be so easy in Kg and grams.

#22 12 feet by 15 feet gives you 180 square feet.
there are 9 square feet in a square yard ,so 180/9 = 20 square yards

#28

set up 2 ratio problems

first the peas:
1/2 cup of peas = 300 cal
2/3 cup of peas = x cal
(1/2)/(2/3) = 300/x

.
.
x = 400

so you want 400 cal to come from the spinach

(1/2)/x = 80/400

solve to get x = 5/2

so 2 1/2 cups of spinach are needed

this is difficult for me...
#5 A carpenter needs 4 boards, each 2 feet 9 inches long. If wood is sold only by the foot, how many feet must he buy? the answer is 11 but how do you get 11?

You need to multiply 4 times 2 3/4 to find the total amount of board feet the carpenter needs. (9 inches is 9/12 or 3/4 of a foot.) Do you get 11 by doing this?

yes I do but how do you get 2 3/4??

I don't get this setting up a ratio buisness???

yes I do but how do you get 2 3/4??

Each board is 2 feet, 9 inches long. A foot has 12 inches, so 9 inches is 9/12 of a foot. This fraction reduces to 3/4. So each board is 2 3/4 feet long.

I don't get this setting up a ratio buisness???

This site explains how to set up a ration and find an unknown.

http://www.purplemath.com/modules/ratio.htm

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