Question

36:(x-3)=54:3 2:3=(5x-7):12 0,45:(x+0,8)=6:20 знайти x із пропорції

Answer 1

Є таке правило: добуток крайніх членів пропорції дорівнює добутку середніх її членів.
1)
$36 \div (x + 3) = 54 \div 3 \\ 54(x + 3) = 36 \times 3 \\ 54x + 162 = 108 \\ 54x = 108 - 162 \\ 54x = - 54 \\ x = - 1.$
2)
$2 \div 3 = (5x - 7) \div 12 \\ 3(5x - 7) = 12 \times 2 \\ 15x - 21 = 24 \\ 15x = 24 + 21 \\ 15x = 45 \\ x = 3$
3)
$0.45 \div (x + 0.8) = 6 \div 20 \\ 6(x + 0.8) = 20 \times 0.45 \\ 6x + 4.8 = 20 \times \frac{45}{100} \\ 6x + 4.8 = \frac{45}{5} \\ 6x = 9 - 4.8 \\ 6x = 4.2 \\ x = 0.7$

Answer 2

To find the value of x in each proportion, we can use the property of proportions that states:

a:b = c:d is equivalent to ad = bc

Let's solve each proportion step by step:

1. 36:(x-3) = 54:3

We have 36:(x-3) = 54:3, which can be written as:

36 / (x - 3) = 54 / 3

Now, cross-multiply:

36 * 3 = 54 * (x - 3)

108 = 54x - 162

Add 162 to both sides:

54x = 108 + 162 54x = 270

Finally, divide by 54 to find x:

x = 270 / 54 x = 5

So, x = 5.

2. 2:3 = (5x-7):12

We have 2:3 = (5x - 7):12, which can be written as:

2 / 3 = (5x - 7) / 12

Now, cross-multiply:

2 * 12 = 3 * (5x - 7)

24 = 15x - 21

Add 21 to both sides:

15x = 24 + 21 15x = 45

Finally, divide by 15 to find x:

x = 45 / 15 x = 3

So, x = 3.

3. 0.45:(x + 0.8) = 6:20

To avoid decimals, we can multiply both sides by 100 to get rid of the decimal point:

100 * 0.45 / (x + 0.8) = 100 * 6 / 20

Now, we have:

45 / (x + 0.8) = 600 / 20

45 / (x + 0.8) = 30

Now, cross-multiply:

45 = 30 * (x + 0.8)

Divide both sides by 30:

x + 0.8 = 45 / 30 x + 0.8 = 1.5

Subtract 0.8 from both sides to find x:

x = 1.5 - 0.8 x = 0.7

So, x = 0.7.

In summary:

1. x = 5
2. x = 3
3. x = 0.7