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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lfryerda | High School Teacher | (Level 2) Educator
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.
lemjay | High School Teacher | (Level 3) Senior Educator
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 .
wescarlyon337 | Student, Grade 10 | (Level 1) Salutatorian
the ball costs $0.05