tim has a large collection of books. the number of paperback books he owns is three less than four times the number of hardcover
2 answers:
We can solve this by setting up a couple of equations.
Let's allow x to represent the number of paperbacks Tim owns, and allow y to represent the number of hardcover books he owns.
Using the information in the question, we can write the equations:
1)
2)
Let's rearrange equation 1 so that it is in standard form:
And then let's multiply equation 2 by 4 so that we can cancel out y when we solve the system of equations:
Then we can add the two equations and solve for x:
1)
+ 2)
------------------------------------
So now we now the number of paperback books Tim has is 357. Let's plug this into one of the original equations to solve for the number of hardcover books (y):
And now we know that Tim owns 90 hardcover books.
Let's allow x to represent the number of paperbacks Tim owns, and allow y to represent the number of hardcover books he owns.
Using the information in the question, we can write the equations:
1)
2)
Let's rearrange equation 1 so that it is in standard form:
And then let's multiply equation 2 by 4 so that we can cancel out y when we solve the system of equations:
Then we can add the two equations and solve for x:
1)
+ 2)
------------------------------------
So now we now the number of paperback books Tim has is 357. Let's plug this into one of the original equations to solve for the number of hardcover books (y):
And now we know that Tim owns 90 hardcover books.
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✳︎ ✳︎ ✳︎ ✳︎ ✳︎ ✳︎ Hello There! :)
To determine whether the two expressions are equivalent, we take the second expression and distribute 2:
2(3x+1)
6x+2=2+6x
And now we know the two expressions are equivalent. If you look, you will remember the Commutative Property that states:
a+b=b+a
In this case, a=6x and b=2.
So we know that the two expressions are equivalent.
Hope this helps! :)