How an author can reveal character development to the readers
1 answer:
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Hey!
To solve this equation, we must first convert the mixed numbers into improper fractions. To do that we'll multiply the denominator by the whole number and add the total to the numerator.
<em>Original Equation :</em>
<em>New Equation {Converted Mixed Numbers Into Improper Fractions} :</em>
Now that we've successfully changed our equation, we'll move onto the next step. Next we'll have change the fractions one more time so that the denominators are the same. To do that we'll multiply two by eight to get sixteen. We'll also be multiplying the top portion of the fraction by eight, because whatever you do to the bottom must also be done to the top; And vise versa.
<em>Fraction Conversion :</em>
So, now that we have our new fraction we can go ahead and plug that into our equation so we can start adding. Remember, we don't add the denominators, just the numerators.
<em>Old Equation :</em>
<em>New Equation {Input New Fraction With Common Denominator} :</em>
<em>Solution {New Equation Solved} :</em>
Now I'm not exactly sure how your instructor will accept your answer, but most prefer the final answer to be in the simplest form. In other words, they don't want it in the form of an improper fraction. They'd most likely rather have it as a mixed number.
<em>New Solution {Converted to a Mixed Number} :</em>
Since the fraction cannot be simplified anymore, this should be our final answer.
<em>So, this means that the answer to the equation is </em> .
Hope this helps!
- Lindsey Frazier ♥
Answer:
The artist should make 15 caricatures and 30 portraits.
Step-by-step explanation:
First, we identify the variables for the problem. In this case, the variables will be:
C=number of caricatures
P= number of portraits.
Next, we can use the variables to make the inequalities that constrain the problem.
We know the artist can't spend more than $360 for supplies and we also know that it costs $4 to make a caricature and $10 to make a portrait, so:
We also know the artist has a limit of time of 20 hours, which is the same as 20*60=1200 minutes to paint. We know it takes her 20 minutes to make a caricature and 30 minutes to make a portrait, so:
and we also know she must make a positive number of caricatures and a positive number of portraits so the other two constrains are:
So we can go ahead and graph them. (see attached picture)
Once we graphed the inequalities we can determine what the corners of the polygon created by the intersection of the shaded areas are, so we proceed and calculate them:
first point:
(0,0)
second point:
4(0)+10P=360
P=36
(0,36)
Third point:
20C+30(0)=1200
C=60
(60,0)
Fourth point:
We multiply the first equation by -5 so we get:
-20C-50P=-1800
20C+30P=1200
------------------------
-20P=-600
P=30
so:
20C+30(30)=1200
20C=1200-900
20C=300
C=15
(15,30)
Once we found the 4 points, we go ahead and evaluate them for the objective function. In this case, the objective function is the total amount of money she got from selling the pieces of art, so we get:
I=10C+20P
Point 1
I=10(0)+20(0)=0
Point 2
I=10(0)+20(36)=720
Point 3
I=10(60)+20(0)=600
Point 4
I=10(15)+20(30)=750
Next, we look for the greatest income which in this case will be 750 so that's why she must make 15 caricatures and 30 Portraits.
