Answer :
Question 1: Get 6 qt of 80% juice with 100% juice and 20% juice.
Change the percents to decimals (.8, 1, and .2)
To model 6 quarts of 80% juice, write as 6(.8)
To model an unknown amount of 20% juice, write as x(.2)
Since there will be a total of 6 quarts, the amount of 100% juice must be 6 quarts minus the amount of 20% juice, which I called 'x'.
Therefore, to model the amount of 100% juice, write it as (6-x)(1)
You can use these to make the equation x(.2)+(6-x)(1)=6(.8)
.2x+6-x=4.8
-0.8x+6=4.8
-0.8x=-1.2
x=1.5
This is the amount of 20% juice. To find the amount of 100%, subtract 1.5 from 6.
6-1.5=4.5. This is the amount of 100% juice to use.
Question 2: Find the flat cost and cost per page if 4 pages costs $5.36 and 7 pages costs $7.88.
Since we know that the flat cost is the same in both, we can model it with the variable 'y'
Also, since the cost per page is the same in both, we can model it with the variable 'x'
Therefore, we know that y+4x=5.36 and that y+7x=7.88
We can use the elimination method to solve for x. To do that, we must have one equation with y and one with -y.
Multiply the first equation by -1 to get -y-4x=-5.36
Eliminate the y's and add the other two
-y-4x=-5.36
y+7x=7.88
3x=2.52
Divide both sides by 3
x=.84
Then, plug x back into one of the equations
y+4(.84)=5.36
Simplify
y+3.36=5.36
Subtract 3.36 from both sides
y=2
Therefore, the flat rate $2 and the cost per page is $0.84
Change the percents to decimals (.8, 1, and .2)
To model 6 quarts of 80% juice, write as 6(.8)
To model an unknown amount of 20% juice, write as x(.2)
Since there will be a total of 6 quarts, the amount of 100% juice must be 6 quarts minus the amount of 20% juice, which I called 'x'.
Therefore, to model the amount of 100% juice, write it as (6-x)(1)
You can use these to make the equation x(.2)+(6-x)(1)=6(.8)
.2x+6-x=4.8
-0.8x+6=4.8
-0.8x=-1.2
x=1.5
This is the amount of 20% juice. To find the amount of 100%, subtract 1.5 from 6.
6-1.5=4.5. This is the amount of 100% juice to use.
Question 2: Find the flat cost and cost per page if 4 pages costs $5.36 and 7 pages costs $7.88.
Since we know that the flat cost is the same in both, we can model it with the variable 'y'
Also, since the cost per page is the same in both, we can model it with the variable 'x'
Therefore, we know that y+4x=5.36 and that y+7x=7.88
We can use the elimination method to solve for x. To do that, we must have one equation with y and one with -y.
Multiply the first equation by -1 to get -y-4x=-5.36
Eliminate the y's and add the other two
-y-4x=-5.36
y+7x=7.88
3x=2.52
Divide both sides by 3
x=.84
Then, plug x back into one of the equations
y+4(.84)=5.36
Simplify
y+3.36=5.36
Subtract 3.36 from both sides
y=2
Therefore, the flat rate $2 and the cost per page is $0.84
The quarts of the two different fruit juices and, the flat and per page fee is required.
The number of quarts of 100% fruit juice is 4.5.
The number of quarts of 80% fruit juice is 1.5.
The flat fee is $2 and the per page fee is $0.84.
Let [tex]x[/tex] be the number of quarts of 100% fruit juice
and [tex]y[/tex] be the number of quarts of 20% fruit juice
The two fruit juices combine to form 6 quarts of fruit juice
[tex]x+y=6[/tex]
The mixture ratios will be
[tex]x+0.2y=0.8\times 6\\\Rightarrow x+0.2y=4.8[/tex]
Subtracting the equations we get
[tex]y-0.2y=6-4.8\\\Rightarrow 0.8y=1.2\\\Rightarrow y=\dfrac{1.2}{0.8}\\\Rightarrow y=1.5[/tex]
[tex]x=6-y=6-1.5\\\Rightarrow x=4.5[/tex]
The number of quarts of 100% fruit juice is 4.5.
The number of quarts of 80% fruit juice is 1.5.
Let [tex]x[/tex] be the number of pages
[tex]y[/tex] be the total cost.
The ordered pairs are
[tex](4,5.36)[/tex] and [tex](7,7.88)[/tex]
Finding equation of line
[tex]y-5.36=\dfrac{7.88-5.36}{7-4}(x-4)\\\Rightarrow y-5.36=0.84x-3.36\\\Rightarrow y=0.84x-3.36+5.36\\\Rightarrow y=0.84x+2[/tex]
The flat fee is $2 and the per page fee is $0.84.
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