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A bat and a ball cost $1.10. The bat costs $1 more than the ball. How much does the...

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oxfbarra2 | eNoter

Posted December 22, 2012 at 7:27 AM via web

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A bat and a ball cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

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

Posted December 22, 2012 at 12:23 PM (Answer #1)

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Let x be the cost of the ball.

Since the bat costs $1 more than the ball, in math form it is:

cost of the bat = x + 1

So the total cost of the bat and the ball is:

cost of the bat  +  cost of ball = 1 .10

`x + 1 + x = 1.10`

Combining like terms yields:

`2x+ 1 = 1.10`

Then, solve for x. To do so, subtract both sides by 1.

`2x+1-1=1.10-1`

`2x=0.10`

And divide both sides by 2.

`(2x)/2=0.10/2`

`x= 0.05`

Hence, the ball costs  $0.05  .

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lfryerda | High School Teacher | (Level 2) Educator

Posted December 22, 2012 at 5:23 PM (Answer #2)

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This is a problem that illustrates how solving equations using algebra can get a solution that may defy a false mathematical intuition.  

Since the bat costs $1 more than the ball, and the two of them together cost $1.10, we would like to know the cost of the ball.  We can set up an algebraic problem to solve this.  Usually we let a variable represent what we are looking for.

Let x be the cost of the ball.

Then setup an equation that combines all the information given:

`x+(x+1)=1.10`  since the ball plus the bat cost $1.10.  Now simplify the left side.

`x+x+1=1.1`   multiply by 10 to get rid of decimals

`10x+10x+10=11`   collect like terms

`20x=11-10`   simplify the right side

`20x=1`   divide

`x=1/20`   express as money

`x=0.05`

The ball costs 5 cents.

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wescarlyon337 | Student, Grade 10 | Salutatorian

Posted January 19, 2013 at 6:20 PM (Answer #3)

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the ball costs $0.05

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