Question

25*(k*8)*20=48000 8000:(25x+50)-15=90-65 (z-12):6+45=211 350:(4y-62)=320-145

Answer 1

25 · (k · 8) · 20 = 48 000

25 · (k · 8) = 48 000 : 20

25 · (k · 8) = 2 400

k · 8 = 2 400 : 25

k · 8 = 96

k = 96 : 8

k = 12

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

8 000 : (25x + 50) - 15 = 90 - 65

8 000 : (25x + 50) - 15 = 25

8 000 : (25x + 50) = 25 + 15

8 000 : (25x + 50) = 40

25x + 50 = 8 000 : 40

25x + 50 = 200

25x = 200 - 50

25x = 150

x = 150 : 25

x = 6

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

(z - 12) : 6 + 45 = 211

(z - 12) : 6 = 211 - 45

(z - 12) : 6 = 166

z - 12 = 166 · 6

z - 12 = 996

z = 996 + 12

z = 1 008

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

350 : (4у - 62) = 320 - 145

350 : (4у - 62) = 175

4у - 62 = 350 : 175

4у - 62 = 2

4у = 2 + 62

4у = 64

у = 64 : 4

у = 16

Answer 2

Let's solve each equation step by step:

1. 25*(k*8)*20 = 48000:

To simplify the equation, we'll start by solving the innermost parentheses first:

k * 8 = 8k

Now we can substitute this value back into the equation:

25 * (8k) * 20 = 48000

Multiplying the numbers inside the parentheses:

200k * 20 = 48000

4000k = 48000

Dividing both sides of the equation by 4000:

k = 48000 / 4000

k = 12

So the value of k is 12.

2. 8000:(25x+50)-15 = 90-65:

Let's simplify this equation step by step:

Inside the parentheses:

25x + 50

Now we can substitute this value back into the equation:

8000 / (25x + 50) - 15 = 90 - 65

To get rid of the fractions, let's find the common denominator, which is (25x + 50):

8000 / (25x + 50) - 15(25x + 50) = (90 - 65)(25x + 50)

Now let's simplify the equation:

8000 - 375x - 750 - 15(25x + 50) = 25x + 25

8000 - 375x - 750 - 375x - 750 = 25x + 25

Combine like terms:

-750x - 1500 = 25x + 25

Add 750x and 1500 to both sides:

-750x - 1500 + 750x + 1500 = 25x + 25 + 750x + 1500

0 = 775x + 1525

Subtract 1525 from both sides:

-1525 = 775x

Divide both sides by 775:

x = -1525 / 775

x ≈ -1.9677

So the value of x is approximately -1.9677.

3. (z-12):6 + 45 = 211:

Let's solve this equation step by step:

First, let's simplify the division:

(z - 12) / 6 + 45 = 211

Now, subtract 45 from both sides:

(z - 12) / 6 = 211 - 45

(z - 12) / 6 = 166

Multiply both sides by 6:

z - 12 = 166 * 6

z - 12 = 996

Add 12 to both sides:

z = 996 + 12

z = 1008

So the value of z is 1008.

4. 350:(4y-62) = 320 - 145:

Let's solve this equation step by step:

First, let's simplify the division:

350 / (4y - 62) = 320 - 145

Now, subtract 320 from both sides:

350 / (4y - 62) - 320 = -145

To get rid of the fraction, let's multiply both sides by (4y - 62):

350 = -145(4y - 62)

Distribute the -145:

350 = -580y + 8970

Subtract 8970 from both sides:

350 - 8970 = -580y

-8620 = -580y

Divide both sides by -580:

y = -8620 / -580

y ≈ 14.8966

So the value of y is