Question

Х+у+z=168 x:y=3:4 y:z=2:7

Answer 1

Пусит x = 3е ; y = 4е ; z = 14е
3е + 4е + 14е = 168
21е = 168
е = 8
x = 3е = 3×8 = 24
y = 4×8 = 32
z = 14×8 = 112
Ответ: 24 ; 32 ; 112

Answer 2

To solve the system of equations:

1. Start by assigning variables to each unknown quantity. Let's use:

   • Let x represent the value of x.
   • Let y represent the value of y.
   • Let z represent the value of z.

2. Use the given information to set up the equations:

   • The first equation is: x + y + z = 168.
   • The second equation is: x/y = 3/4.
   • The third equation is: y/z = 2/7.

3. Solve the second equation for x in terms of y: Multiply both sides of the equation by y: x = (3/4) * y.

4. Solve the third equation for z in terms of y: Multiply both sides of the equation by z: y = (2/7) * z.

   Cross-multiply: 7y = 2z.

   Divide both sides of the equation by 7: y = (2/7) * z.

5. Substitute the value of x and y from equations 3 and 4 into equation 1: (3/4) * y + y + y = 168.

   Simplify: (3/4 + 1 + 1) * y = 168.

   Convert the fractions to a common denominator: (3/4 + 4/4 + 4/4) * y = 168.

   Combine the fractions: (11/4) * y = 168.

   Multiply both sides by 4/11 to isolate y: y = (168 * 4/11).

   Calculate y: y = 168 * 4/11 = 672/11.

6. Substitute the value of y into equations 3 and 4 to find x and z: x = (3/4) * (672/11) = 2016/44 = 288/11. z = (2/7) * (672/11) = 2688/77.

Therefore, the solution to the system of equations is: x = 288/11, y = 672/11, z = 2688/77.