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Q: X varies directly with y and z x equals 40 when y equals 10 and z equals 20 Find x when y equals 30 and z equals 40?

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40

y = -5

y = 8

1

x = 5.y.z so 5.10.12 = 600

50

m = 24

y = kx: 10 = 37k so k = 10/37 and y = 10x/37

We write y=kx since y varies directly as x. Now we know if x is 5, y is 10. so we write 10=5k so k=2

The answer is x=10. If: x=20 y=8 z=4 then: y=8/2=4 z=4*2=8 since x varies directly with y, meaning whatever happens to y, happens to x, so if y was divided by 2, then x should be divided by 2. After all, the inverse of division is multiplication.

x = 75

y = x/k so 15 = 6/k making k = 0.4. when x = 10 y = 10/0.4 ie 25 alternatively y/x = k ie 15/6 = k so k = 2.5; y/10 = 2.5 making y = 25.

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