What is the value of r in the equation 3r − 6 = 18?
2 answers:
Answer:
B.) 8
Step-by-step explanation:
3r - 6 = 18
First, we take -6 to the other side of the equals to sign (=), where it changes to +6.
3r = 18+6
Now we add the LHS.
3r = 24
Now, we take 3 to the other side of =, where it will represent the denominator.
r =
We now solve the fraction which on dividing, comes as 8.
r = 8.
You might be interested in
Let s denote the number of pages in each issue of the sports magazine.
Let t denote the number of pages in each issue of the technology magazine.
Given that a sports magazine prints 12 issues per year and a technology magazine prints 10 issues per year.The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year.
This can be written in equation as,
Since, it is given that, "Each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine".
This can be written in equation as,
Thus, the set of equations that represent the given data is
and
Hence, Option A is the correct answer.
<h3>Answer:</h3>
- 8 pieces
- 3/8 foot
a) Let n represent the number of 1 7/8 ft pieces. Then we have ...
... 16 1/2 ft = n × (1 7/8 ft)
We can find n by dividing this equation by 1 7/8.
... (16 1/2)/(1 7/8) = n = (132/8)/(15/8) = 132/15
... n = 8 12/15 = 8 4/5
The integer number of pieces that can be cut is 8 pieces.
b) The length of the left-over piece is 4/5 of the full length of a piece, so is ...
... (4/5) × (15/8 ft) = 12/8 ft
We want to divide this into 4 equal lengths, so each of those lengths will be 1/4 of the length of the left-over:
... (1/4) × (12/8 ft) = 3/8 ft
_____
<em>Comment on arithmetic with fractions</em>
This problem is easier if you <em>convert the mixed numbers to improper fractions</em>. This is done by expressing the integer as a number of fractional parts, then adding the fraction part of the mixed number:
... a + b/c = (a×c/c) + b/c = (ac +b)/c
Division with fractions is taught a couple of different ways. One way you can do it is to "invert and multiply". That is, you multiply the numerator fraction by the reciprocal of the denominator fraction:
... (a/b)/(c/d) = (a/b)×(d/c)
Another way you can do the division is to express each of the numerator and denominator fractions over the same denominator. Then the quotient is the ratio of numerators.
... (a/c)/(b/c) = a/b
This is the method we used here. Effectively, we converted 16 1/2 to 16 4/8 then to (16×8 +4)/8 = 132/8. Then the numerator and denominator fractions both had denominators of 8, so (132/8)/(15/8) = 132/15. This fraction can be reduced by removing a factor of 3 from numerator and denominator to give ...
... 132/15 = 44/5 = 8 4/5