Question

92=x+y+z x:y=одна третья :4 y:z=6:5

Answer 1

Ответ:

Ответ: х = 4; у = 48; z = 40.

Пошаговое объяснение:

Х + y + z = 92

x : y = (1/3) : 4 = 1 : 12;     =>,  что y = 12х.

y : z = 6 : 5;    =>,   что z = 5у/6  или z = 5*12х/6 = 10х.

х + 12х + 10х = 92

23х = 92

х = 92 : 23

х = 4

у = 12 * 4 = 48

z = 10 * 4 = 40

Ответ: х = 4; у = 48; z = 40.

Answer 2

To solve the system of equations, let's use the given information:

1. x + y + z = 92 (Equation 1)
2. x : y = 1/3 : 4 (Equation 2)
3. y : z = 6 : 5 (Equation 3)

We'll start by expressing the ratios in Equations 2 and 3 as fractions:

Equation 2: x : y = 1/3 : 4 can be rewritten as x/y = 1/3 * 1/4 = 1/12. Equation 3: y : z = 6 : 5 can be rewritten as y/z = 6/5.

Now, we have a system of three equations:

1. x + y + z = 92
2. x/y = 1/12
3. y/z = 6/5

Let's solve the system step by step:

Step 1: Solve Equation 2 for x in terms of y: x/y = 1/12 x = (1/12) * y

Step 2: Solve Equation 3 for y in terms of z: y/z = 6/5 y = (6/5) * z

Step 3: Substitute the expressions for x and y from Steps 1 and 2 into Equation 1: (1/12) * y + y + (6/5) * z = 92

Step 4: Find a common denominator for the fractions: Multiply the whole equation by 60 (a common multiple of 12 and 5) to eliminate the denominators:

60 * ((1/12) * y) + 60 * y + 60 * ((6/5) * z) = 60 * 92

Step 5: Simplify and solve for y: 5y + 60y + 72z = 5520 65y + 72z = 5520 65y = 5520 - 72z y = (5520 - 72z) / 65

Step 6: Substitute the value of y back into the equation for x to find its value: x = (1/12) * y x = (1/12) * (5520 - 72z) / 65

Step 7: Use the values of x and y to find z from Equation 1: x + y + z = 92 ((1/12) * (5520 - 72z) / 65) + ((5520 - 72z) / 65) + z = 92

Step 8: Simplify and solve for z: [5520 - (72z)/65 + 65(5520 - 72z)] / 65 = 92

Step 9: Solve for z: [5520 - (72z) + 65(5520 - 72z)] = 92 * 65 5520 - 72z + 358800 - 4680z = 5980

Step 10: Continue solving for z: 5520 + 358800 - 5980 = 72z + 4680z 364340 = 4752z z = 364340 / 4752 z ≈ 76.68

Step 11: Find x and y using the values of z: y = (5520 - 72z) / 65 ≈ (5520 - 72 * 76.68) / 65 ≈ 46.77 x = (1/12) * (5520 - 72z) / 65 ≈ (1/12) * (5520 - 72 * 76.68) / 65 ≈ 3.24

So, the approximate values of x, y, and z are: x ≈ 3.24 y ≈ 46.77 z ≈ 76.68