Hi there! The unit rate per carton is $4.
To find our answer we must divide the total cost by the total cartons bought.
$ 48 / 12 = $4
Linear equations are all solved the same way. Figure out the operations performed on the variable. Undo those in reverse order.
Here, the variable is
- divided by 2
- has -7 added.
In reverse order, we undo these operations by
- adding 7
- multiplying by 2.
Whatever we do to one side of an equation, we must also do to the other side. That is how the equal sign remains valid.
2 = m/2 -7
2 +7 = m/2 -7 +7 . . . . . add 7
9 = m/2 . . . . . . . . . . . . simplify
2*9 = 2*m/2 . . . . . . . . multiply by 2
18 = m . . . . . . . . . . . . . simplify. (You know that 2/2 = 1, and m*1 = m.)
The answer is m = 18.
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Check:
.. 2 = 18/2 -7
.. 2 = 9 -7 . . . . . . . true. The answer checks OK.
To "rationalize the denominator" is another way to say, getting rid of that pesky radical at the bottom.
we'll simply start by multiplying top and bottom by the "conjugate" of the denominator, recall difference of squares, anyhow, let's do so
Answer: girls=20, sister=10
Step-by-step explanation:
Let x = the girl's sister's age (present)
Let 2x= the girl's age (present)
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According to the question
(x+5)(2x+5)=375
Expand parentheses by FOIL (First Outer Inner Last)
2x²+5x+10x+25=375
Combine like term (5x and 10x)
2x²+15x+25=375
Subtract 375 on both sides
2x²+15x+25-375=375-375
2x²+15x-350=0
Find the factors (cross factor)
(x-10)(x+17.5)=0
x=10 or x=-17.5 (rej) ⇔ the age can't be negative
the girl's age is 20, and her sister's age is 10.
