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Expand brackets on both sides:  4m − 8 = 5mt + 3t

Collect all terms containing 'm' to one side of the equation: 4m − 5mt = 8 + 3t

Factorise the terms containing 'm': m (4 − 5t) = 8 + 3t

We have a right angle triangle in this problem. We can use Pythagoras' theorem - the square of the hypotenuse is equal to the sum of the squares of the other two sides of the right angle triangle...

Firstly start by rearranging [equ1] to get y = 2x + 1 . Then substitute this result into [equ2] this will give you (2x + 1) (2x ) x . Simplify the equation and subtract two from both sides to 2 − x + 1 + ...

1. Find by what ratio the weigh of rice has increased.

If the rice increases in weight from 60g to 145g, the factor by which it increases is: (145/60) = 2.4166...

2. M...

There are a few ways to tackle this particular style of problem. First off we can try doing it without using any bracket theory and just focus on the raw numbers (a somewhat simpler approach). Step 1: We'...