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You spent $600 on bags. Some bags cost $1, the others cost $2 each. If you bought twice...

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ogidi | Student | Honors

Posted November 27, 2012 at 10:29 AM via web

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You spent $600 on bags. Some bags cost $1, the others cost $2 each. If you bought twice as many $1 bags as $2 bags, how many were ordered in total?

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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted November 27, 2012 at 11:28 AM (Answer #1)

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Let x be the number of $1 bags that we bought.

An, let y be the number of $2 bags that we bought.

So the total cost equation is:

`$1x+$2y=$600`

We may re-write this as:

`x + 2y = 600`

Since the number of $1 bags (x) is twice the number of $2 bags (y), then:

`x = 2y`

Substitute this to the total cost equation.

`x+2y=600`

`2y+2y=600`

`4y=600`

Divide both sides by 4, to isolate the y.

`(4y)/4=600/4`

`y=150`

So, we bought 150 pieces of $2 bag.

Then, substitute this to x = 2y.

`x= 2(150)=300`

And, we ordered 300 pieces of $1 bag.

Then, add the values of x and y to get the total number of bags.

`x + y = 300+150 = 450`

Hence, we bought a total of 450 bags.  

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 27, 2012 at 1:19 PM (Answer #2)

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The total amount spent on the bags was $600. Some of them cost $1 and the others $2. If the number of $1 bags bought was X and it is given that twice as many $1 bags were bought as $2 bags, the number of $2 bags bought was X/2.

The total cost of the bags in terms of X is 1*X + 2*(X/2). Equate this to 600 and solve for X.

X + X = 600

=> X = 300

The total number of bags was X + X/2 = 300 + 150 = 450

The total number of bags bought was 450

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kashmirinnocence | Student , Undergraduate | Honors

Posted November 27, 2012 at 10:58 AM (Answer #3)

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let the no.of  bags that cost $1 be x

let the no.of bags that cost $2 be y

acc to Q, X=2Y( you bought twice as many $1 bags as $2 bags) (1)

ALSO 1(X)+2Y=600 (You spent $600 on bags)(2)

USE (1) IN (2)

2Y+2Y=600

which implies 4y=600

i.e,y=150

use this value in (1) we get,x=2(150)=300

so we bought 300+150 =450 in total

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