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Home > Algebra calculators > Variation equations example - x proportion y and x=4,y=2. find x=18,y=?.
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2. Variation equations - If `x prop y` and x=4,y=2 then find y when x=18 example
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1. Examples
1. `x prop y and x=4,y=2.` Find `x=18,y=?`
Solution:
`x prop y`
`=>x=K*y`
Now, `x=4,y=2`
`=>4 = K * 2`
`=> K = (4)/(2)`
`=> K = 2`
Hence, `x=2*y`
`x=18,y=?`
`=>18=2 * y`
`=> (18)/(2) = y`
`=>y=9`
2. `x prop yz and x=8,y=4,z=3.` Find `x=?,y=6,z=4`
Solution:
`x prop yz`
`=>x=K*yz`
Now, `x=8,y=4,z=3`
`=>8 = K * 4*3`
`=>8 = K * 12`
`=> K = (8)/(12)`
`=> K = 2/3`
Hence, `x=2/3*yz`
`x=?,y=6,z=4`
`=>x=2/3 * 6*4`
`=>x=2/3 * 24`
`=>x=16`
3. `x prop y^3/z and x=8,y=4,z=3.` Find `x=?,y=6,z=4`
Solution:
`x prop y^3/z`
`=>x=K*y^3/z`
Now, `x=8,y=4,z=3`
`=>8 = K * 4^3/3`
`=>8 = K * 64/3`
`=> K = 8*3/64`
`=> K = 3/8`
Hence, `x=3/8*y^3/z`
`x=?,y=6,z=4`
`=>x=3/8 * 6^3/4`
`=>x=3/8 * 54`
`=>x=81/4`
This material is intended as a summary. Use your textbook for detail explanation.
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