An equivalent fraction in higher terms is 9/12 because you must multiply the top by 3 because you multiplied the bottom by 3
Answer: One plain roll is 4 dollars and one shiny roll is 6 dollars.
Step-by-step explanation:
lets start by saying
rolls of plain wrapping paper = x
rolls of shiny wrapping paper = y
Kathryn sold 4 plain rolls and 3 shiny rolls for 34 dollars.
4x+3y=34
Eugene sold 4 plain rolls and 2 shiny rolls for 28 dollars
4x+2y=28
Both equations will look like this.
4x+3y=34
-1(4x+2y)=(28)-1
we can multiply the second equation by -1 to get y alone. (doesn't matter which equation). Once you do that, the positive 4x and the negative 4x cancel out, 3y-2y=1y and 34-28=6. you are left with
1y=6 so one shiny roll is 6 dollars.
now use that price to find the cost of the plain roll.
lets use Kathryn's equation
4x + 3(6)=34
4x + 18= 34
-18 -18
4x=16. Divide by 4 to find cost of one plain roll.
16÷4=4. One plain roll costs 4 dollars.
Lets check. Using Kathryn's equation,
4(4) + 3(6)=34
16+18=34
34=34. We are right.
X+15 = 3x - 7 => 22 = 2x => x=11
Factor
7
x
7
x
out of
14
x
2
14
x
2
.
7
x
(
2
x
)
−
21
x
7
x
2
x
-
21
x
Factor
7
x
7
x
out of
−
21
x
-
21
x
.
7
x
(
2
x
)
+
7
x
(
−
3
)
7
x
2
x
+
7
x
-
3
Factor
7
x
7
x
out of
7
x
(
2
x
)
+
7
x
(
−
3
)
7
x
2
x
+
7
x
-
3
.
7
x
(
2
x
−
3
)
Answer:
To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
<h2>
</h2>
Simplify
<h2>
</h2>
We have the final answer as
<h2>
</h2>
Hope this helps you
