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vovangra [49]
3 years ago
11

Solve for x,W 3x+3W-66 (1) 7 12x+15W-300 (2)

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
3 0

Answer:

x=10 and W=12

Step-by-step explanation:

Let's solve the equations. First we need to understand that the problem can be solved because we have two variables (x, W) and two equations.

Now, we have the following equations:

3x+3W-66 making the equation equal to 0:

3x+3W-66=0 which can be express as:

3x=-3W+66

x=(-3W+66)/3

x=-W+22 (equation 1)

The next equation is:

12x+15W-300 making the equation equal to 0 and then divided by 3:

(12x+15W-300)/3=0 which is:

4x+5W-100=0 (equation 2), using equation 1 we can write:

4(-W+22)+5W-100=0

-4W+88+5W-100=0

W-12=0

W=12

Using W=12 in equation 2 we have:

4x+5W-100=0

4x+5*(12)-100=0

4x+(60)-100=0

4x-40=0

4x=40

x=40/4

x=10

In conclusion the solution for the equations are: x=10 and W=12.

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Step-by-step explanation:

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3 years ago
There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r
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Answer:

12

Step-by-step explanation:

The first cave has 7 times more bats than the last cave.  So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves.  So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats.  Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end.  If cave #45 has b bats, then caves #39-#44 have 77−b bats.  And since caves #38-44 have 77 bats, then cave #38 has b bats.  Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

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There are at most 12 bats in the 30th cave.

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