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aksik [14]
3 years ago
5

Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?

Mathematics
2 answers:
makkiz [27]3 years ago
5 0

Hello from MrBillDoesMath!

Answer:

x = 7/8

Discussion:

3[x + 3(4x – 5)] = 15x – 24 =>

3x + (3*3)(4x-5) = 15x - 24  =>

3x + 9*(4x) - (3*3)*5 = 15x - 24 =>

3x + 36x  - 45 = 15x - 24  =>   (add 24 to each side)

3x + 36x - 45 + 45 = 15x - 24 + 45 =>

39x = 15x + 21  =>                    (as 45-24 = 21)

39x-15x = 21 =>                        (subtract 15x from both sides)

24x = 21 =>

x = 21/24 = -7/8


Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!


Anastaziya [24]3 years ago
4 0
I hope this will help

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Then, we also must know the formula for area of a cube

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Area=6a^2

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Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the c
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2 years ago
A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening
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Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

C+S+A=750

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

3C+5S+7A=3450

This equation represents the totaled receipts.

The system :

C+S+A=750\\3C+5S+7A=3450

has the following associated matrix :

\left[\begin{array}{cccc}1&1&1&750\\3&5&7&3450\end{array}\right]

By performing elementary matrix operations we find that the matrix is equivalent to

\left[\begin{array}{cccc}1&0&-1&150\\0&1&2&600\\\end{array}\right]

The new system :

C-A=150\\S+2A=600

Working with the equations :

C = 150 + A\\S = 600-2A

Our solution vector is :

\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]

For example :

If 0 adults attended ⇒ A = 0

C = 150 + 0 \\C = 150\\S = 600 - 2A\\S = 600

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S = 600 -2A

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

7 0
3 years ago
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