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Dimas [21]
3 years ago
5

Ten times the sum of half a number and 6 is 8

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
5 0

Even though we don't know the number yet, we need to give it some kind of label
so that we can work with it.  We can call it anything.  I'd like to call it ' G '.

The number we're looking for is ' G '.

Half of it is  1/2 G

The sum of that and 6 is          1/2 G + 6

Ten times that is              10 (1/2 G + 6)

The question says that's 8.
                                        So       10 (1/2 G + 6) = 8

Divide each side by  10 :                1/2 G + 6  =  0.8

Subtract  6  from each side:            1/2 G  =  - 5.2

Multiply each side by  2 :                        G  =  - 10.4

That seems like a weird answer.  We should check it.

The number:                                         -10.4
Half the number:                                   - 5.2
The sum of half the number and 6:      -5.2 + 6 = +0.8
Ten times that sum:                                                  8

Yep !  By golly, sho nuff, dV-dT and E to the X !  
Everything checks out, and the mystery number is      - 10.4

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Find the value of 5x-6 given that 2x-7=9​
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34

Step-by-step explanation:

Given that

2x - 7 = 9 ← solve for x

Add 7 to both sides

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into 5x - 6

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A concert hall has 8,000 seats and two categories of ticket prices, $29 and $34. Assume that all seats in each category can be s
Greeley [361]

Using a system of equations, it is found that:

  • For a profit of $255,000, 3400 tickets of $29 and 4600 tickets of $34 must be sold.
  • For a profit of $271,000, 200 tickets of $29 and 7800 tickets of $34 must be sold.
  • For a profit of $235,000, 7400 tickets of $29 and 600 tickets of $34 must be sold.

--------------------

The variables of the system are:

  • x, which is the number of $29 tickets sold.
  • y, which is the number of $34 tickets sold.

Total of 8,000 seats, all can be sold, thus:

x + y = 8000 \rightarrow x = 8000 - y

--------------------

For a profit of $255,000, we have that:

29x + 34y = 255000

29(8000 - y) + 34y = 255000

5y = 23000

y = \frac{23000}{5}

y = 4600

x = 8000 - 4600 = 3400

For a profit of $255,000, 3400 tickets of $29 and 4600 tickets of $34 must be sold.

--------------------

For a profit of $271,000, we have that:

29x + 34y = 271000

29(8000 - y) + 34y = 271000

5y = 39000

y = \frac{39000}{5}

y = 7800

x = 8000 - 7800= 200

For a profit of $271,000, 200 tickets of $29 and 7800 tickets of $34 must be sold.

--------------------

For a profit of $235,000, we have that:

29x + 34y = 235000

29(8000 - y) + 34y = 235000

5y = 3000

y = \frac{3000}{5}

y = 600

x = 8000 - 600 = 7400

For a profit of $235,000, 7400 tickets of $29 and 600 tickets of $34 must be sold.

A similar problem is given at brainly.com/question/22826010

3 0
3 years ago
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