SOLUTION: Dear Tutor/or Tutors, I would greatly appreciate it if you can help me solve the following problem and let me know how you did so; 5 more than two thirds of the number is the s

Question 97639: Dear Tutor/or Tutors,
I would greatly appreciate it if you can help me solve the following problem and let me know how you did so;
5 more than two thirds of the number is the same as 3 less than one half of the number.
Thank You Very Much!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The number you are looking for is unknown. So call it x.
.
Two-thirds of the number is:
.

.
and 5 more than that is written as:
.
<=== left side of the equation we are working toward
.
That is the same (meaning equal to) 3 less than one-half the number. One-half the number is:
.

.
and 3 less than that is:
.
<=== right side of the equation we are getting
.
So now we have two sides that are to be equal. In equation form this is:
.

.
Let's get rid of the fractions by multiplying both sides of this equation (all terms) by
a common denominator of 6. (Note that we get 6 by multiplying the two denominators of
3 and 2). Multiplying both sides of the equation (all terms) by 6 results in the equation
becoming:
.

.
Doing the division in the two sets of parentheses simplifies the equation to:
.

.
Get rid of the 3x on the right side by subtracting 3x from both sides. When you do that
the equation reduces to:
.

.
Now get rid of +30 on the left side by subtracting 30 from both sides to end up with:
.

.
That's the answer. Let's check it by using it in the original problem statement.
.
One-third of -48 is -16. So two-thirds of -48 is -32. 5 more than -32 is - 27 (-32 + 5 = -27).
.
That is to be equal to 3 less than one-half the number. One-half of -48 is - 24 and if you take
away 3 from -24 you have (-24 - 3) -27. So the answer of -27 works because it makes both
sides of the equation equal to -27.
.
Hope this helps you to understand this problem. Getting rid of the fractions is a technique
that often saves you from the complexity of multiplying, dividing, adding, and subtracting
in fractional form. Hope that helps.
.
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