Question

SOLVE EACH PROBLEM. COPY AND ANSWER WITH COMPLETE SOLUTION. (By 2's)

1. z varies jointly as x and y. If z=45 when x=3 and y=5, find z when x=6 and y=9.
2. d varies jointly as e and f. If d=100 when e=2 and f=25. Find d when e=4 and f=6
3. If a varies directly as b and inversely as c. and a=18 when b=24 and c=4, Find a when b=35 and c=5
4. If d varies directly as e and inversely as f. and d=21 when e=27 and f=9, Find d when e=32 and f=8
5. If g varies directly as h and inversely as i, and g=48 when h=36 and i=3, find g when h=18 and i=2

Answer 1

1. z = 162 when x = 6 and y = 9 in joint variation. 2. d is 48 for e = 4 and f = 6 in joint variation. 3. In combined variation, a = 21 for b=35 and c=5. 4. d = 28 5. g = 36.

How to solve variation equations?

1. Using the joint variation formula, z = kxy, where k is the constant of variation:

45 = k × 3 × 5

Solving for k, k = 3. Now, for x = 6 and y = 9:

z = 3 × 6 × 9

z = 162

2. Using the joint variation formula, d = kef, where k is the constant of variation:

100 = k × 2 × 25

Solving for k, k = 2. Now, for e = 4 and f = 6:

d = 2 × 4 × 6

d = 48.

3. Using the combined variation formula,
`\(a = (k \cdot b)/(c)\)`, where k is the constant of variation:

`\[18 = (k \cdot 24)/(4)\]`

Solving for k, k = 3. Now, for b = 35 and c = 5:

`\[a = (3 \cdot 35)/(5) = 21.\]`

4. Using the combined variation formula,
`\(d = (ke)/(f)\)`, where \(k\) is the constant of variation:

`\[21 = (k \cdot 27)/(9)\]`

Solving for k, k = 7. Now, for e = 32 and f = 8:

`\[d = (7 \cdot 32)/(8) = 28.\]`

5. Using the combined variation formula,
`\(g = (kh)/(i)\)`, where k is the constant of variation:

`\[48 = (k \cdot 36)/(3)\]`

Solving for k, k = 4. Now, for h = 18 and i = 2:

`\[g = (4 \cdot 18)/(2) = 36.\]`