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Baseball Math Downside:
If the value of a bat and ball collectively is $1.10 and the bat prices $1 greater than the ball.
Then how a lot is the ball?
Take 30 seconds to resolve this math downside.
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Reply:
The reply shouldn’t be $0.10!
This downside is difficult. At a look, one would simply assume the ball will price 10 cents since $1.10 – $1.00 is 0.10. However that is incorrect.
I am positive this may be solved utilizing instinct and easy arithmetic.
However right here in Apptato we like doing issues the exhausting means.
(This can be a good introduction to Algebra for freshmen)
So let’s remedy this utilizing some algebra.
Let x be the value of the bat and y be the value of the ball.
We all know that the value of the bat and ball collectively is $1.10,
So we create the primary equation: x + y = 1.10
And we additionally know that the value of the bat is $1.00 greater than the ball.
We are able to characterize it within the second equation:
x – y = 1.00, which simply means the value distinction is $1.00 with x (value of the bat) being the better of the two.
We now see a pair of equations generally known as simultaneous equations.
x + y = 1.10
x – y = 1.00
When there are 2 or extra equations we’re capable of the sum of all of the parts of the left facet and equate it to the sum of all of the parts of the fitting facet. The equality is preserved.
The sum or summation is signified by the greek letter capital Sigma.
Including each equations:
On the left facet: x + x is 2x, y – y is 0
whereas on the fitting facet: 1.10 + 1.00 = 2.10
2x = 2.10
x = 1.05
So the bat prices 1.05.
Substituting x again into both equation (let’s go along with the second)
x – y = 1.00
1.05 – y = 1.00
y = 0.05
That is simply the identical as saying: for the reason that bat is 1.05 and is 1.00 greater than the ball subsequently the ball is $0.05.
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