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Simultaneous equations pop up all the time in maths, science, and engineering, so being able to solve them is really useful. Although they can look a bit daunting at first, the same general rules apply...

From the rules of logarithms, we know that:

log(A) - log(B) = log(A/B)

and thus:

log(1-x) - log(x) = log[(1-x)/x]

...

The first term is x, and if it increases by 5 each time then the second term is x+5, third is x+10, and the fourth is x+15.

Adding these values together we get 4x+5+10+15, and this equals...

To answer this question we need to divide the hours needed to complete work (200) by how much a person works a week (35). The key aspect of this question that catches people out is that when dividing 2...

Note here: u_n indicates u subscript n.

(a) u_1 = 48 and the ratio, r = 0.6

Using a calculator, u_2 = 48 x 0.6 = 28.8

u_3 = 28.8 x 0.6 = 17.28

(b...