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ehidna [41]
3 years ago
15

An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $30 for each lawn seat. There are th

ree times as many seats in Section B as in Section A. The revenue from selling all 23,000 seats is $870,000. How many seats are in each section of the amphitheater?
Mathematics
1 answer:
Ratling [72]3 years ago
3 0
<span>Section A seats = 1500 Section B seats = 4500 Lawn seats = 17000 Let's write a few equations to express what we know. A = number of seats in section A B = number of seats in section B L = number of law seats "There are three times as many seats in Section B as in Section A" B = 3A "all 23,000 seats" L = 23000 - A - B L = 23000 - A - 3A "The revenue from selling all 23,000 seats is $870,000" 870000 = 30L + 55B + 75A Now let's substitute 3A for B 870000 = 30L + 55(3A) + 75A And substitute (23000 - A - 3A) = (23000 - 4A) for L 870000 = 30(23000 - 4A) + 55(3A) + 75A And solve for A 870000 = 30(23000 - 4A) + 55(3A) + 75A 870000 = 690000 - 120A + 165A + 75A 870000 = 690000 + 120A 180000 = 120A 1500 = A So we know that section A has 1500 seats. Because of B = 3A = 3*1500 = 4500, section B has 4500 seats. Finally, L = 23000 - A - B = 23000 - 1500 - 4500 = 17000 seats</span>
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Answer:3/4


Step-by-step explanation:

if you divide 21 by 28 you get 3/4

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Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she don
blagie [28]

Given:

  • $35 is charged per form, but $0 if only the easiest form is filed.
  • $2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
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  • Total amount donated for the full year = $1242

To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.

Concept:

We can make use of the Unitary Method here. <u>Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.</u>

So,

<u>Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group</u>


Explanation & Calculation:

We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.

So, putting in the values into the expression,

$35 = $7245 ÷ number of $35 forms

Therefore, number of $35 forms = $7245 ÷ $35

Using simple division, number of $35 forms = 207

Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).

If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.

So, putting the values into the expression,

$2 = $1242 ÷ total number of forms

Therefore, total number of forms = $1242 ÷ $2

Using simple division, total number of forms = 621


Conclusion:

Sterre has filed <u>a total of 621 tax returns</u> (both charged and for free).

Of these 621 returns filed, <u>for 207 forms, Sterre charged $35</u>.

The number of returns Sterre filed for free (that is, the easiest forms) is

Total number of forms - Chargeable forms = 621 - 207 = 414

Thus, Sterre filed <u>414 tax returns for free</u>.


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Fractions that have the same number on the bottom have a "common denominator."
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