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2 years ago

Is 2(x - 3) equals 2x plus 5 a solution

Mathematics

1 answer:

Aneli [31]2 years ago

7 0

2(x - 3) = 2x + 5 Distribute/multiply 2 into (x - 3)

2x - 6 = 2x + 5 Add 6 on both sides

2x = 2x + 11 Subtract 2x on both sides

2x - 2x = 11

0 = 11

This is not a solution because they have to be equal to each other or the same on both sides of the equation

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2 years ago

How many liters of 60% alcohol solution should be added to 40 liters of a 20% alcohol solution to make a 50% solution?

kolbaska11 [484]

Answer:

120 liters of 60% alcohol solution is needed

Step-by-step explanation:

Let's assume

x liters of 60% alcohol solution is added

so, we get solution as

$=\frac{60}{100}\times x$

$=0.6x$

we are given

40 liters of a 20% alcohol solution is

$=40\times\frac{20}{100}$

$=8$

so, total alcohol solution is

$=8+0.6x$

now, we can find total solutions

total solutions is

$=x+40$

now, it is making 50% solution

so, we get

$\frac{8+0.6x}{x+40} =\frac{50}{100}$

now, we can solve for x

$\left(8+0.6x\right)\cdot \:100=\left(x+40\right)\cdot \:50$

$800+60x=50x+2000$

$10x=1200$

$x=120$

So,

120 liters of 60% alcohol solution is needed

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2 years ago

Peter is the owner of a hotel. He has found that when he charges the nightly cost of $139, the average occupancy is 275. In addi

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Answer:

Without price increase, Cost/night = $119

Average occupancy = 372 The revenue will be 119*372 = $44,268

For every $15 price increase, the occupancy decreases by 25. Therefore with x price increases, The revenue will be $(119 + 15x)*(372 25x)

Cost/night = $119 + 15x Occupancy = 372 - 25x

Answer:

The nightly cost with x $15 price increases is $119 + 15x.

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