Chloe charged for admission to her play on three different nights. Each night, a
1 answer:
Answer:
The number of people in total that came to the three showings is 138 people
Step-by-step explanation:
The amount Chloe collected each night for admission to her play = $541
The admission charge for each child = $9
The admission charge for each adult = $17
The number of people attending the play each of the three nights are different
Let x represent the number of children that attend the play on the first night and ley y represent the number of adults that attend, we have;
9·x + 17·y = 541
For the second night, we have;
9·a + 17·b = 541
For the third night, we have;
9·c + 17·d = 541
27·(x + a + c) + 51·(y + b + d) = 1,623
Using Microsoft Excel, where we create a series with the first term = 541 and the common difference, d = -9 and number the adjacent column serially from 1 to 61 and the on the right column we divide the created series by 17 then we search for the whole number combinations, we get three possible combinations as follows;
12 children and 26 adults
29 children and 17 adults
46 children and 8 adults
Therefore, the number of people in total that came to the three showings = 12 + 26 + 29 + 17 + 46 + 8 = 138
The number of people in total that came to the three showings = 138 people.
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Notation
I imagine that the expression you are asked to work with is:
When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.
PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.
This gives us:
To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.
PART B
Start with the answer in part A. Namely,
. For now let's focus only on what is in the parenthesis. We have four terms so let's take them two at a time. I am separating the expression in two using square brackets. ![[( x^{3}+5x)]-[3 x^{2} -15]](https://tex.z-dn.net/?f=%5B%28%20x%5E%7B3%7D%2B5x%29%5D-%5B3%20x%5E%7B2%7D%20-15%5D)
Let's next factor what is in each bracket:
![[( x^{3}+5x)]-[3 x^{2} -15] = [x( x^{2} +5)]-[3( x^{2} +5)]](https://tex.z-dn.net/?f=%5B%28%20x%5E%7B3%7D%2B5x%29%5D-%5B3%20x%5E%7B2%7D%20-15%5D%20%3D%20%5Bx%28%20x%5E%7B2%7D%20%2B5%29%5D-%5B3%28%20x%5E%7B2%7D%20%2B5%29%5D)
Notice that both brackets have the same expression in them so now we factor that out:![[x( x^{2} +5)]-[3( x^{2} +5)] = (x-3)( x^{2} +5)](https://tex.z-dn.net/?f=%20%5Bx%28%20x%5E%7B2%7D%20%2B5%29%5D-%5B3%28%20x%5E%7B2%7D%20%2B5%29%5D%20%3D%20%28x-3%29%28%20x%5E%7B2%7D%20%2B5%29)
Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get:
I imagine that the expression you are asked to work with is:
When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.
PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.
This gives us:
To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.
PART B
Start with the answer in part A. Namely,
Let's next factor what is in each bracket:
Notice that both brackets have the same expression in them so now we factor that out:
Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get: