a) A twenty – kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.
(b) If \(\frac{5}{6}\) of a number is 10 greater than \(\frac{1}{3}\) of it. find the number
(c) Find the equation of the line which passes through the points (2, \(\frac{1}{2}\)) and (-1, -\(\frac{1}{2}\)
Explanation
(a) it will take 1 boy 10m days and when 4 more boys are added, it will take 8(m + 4) days. Since the rate of consumption was the same, then 10m = 8m + 32 and when solves, m = 16
(b) Let x be the number. so that \(\frac{5}{6}\)x = 10 + \(\frac{1}{2}\)x and multiplying through by 6 to get 5x = 60 + 2x. This was solved to get x = 20
(c) Let the gradient be m = \(\frac{\frac{1}{2} - (\frac{1}{2})}{2 - (-1)} = \frac{2}{3}\). The equation of the lines is y - y\(_1\) = m(x - x\(_1\)). Sunstituting for x\(_1\) and y\(_1\)
y - (\(\frac{-1}{2}\)) = \(\frac{1}{2}\)(x - (-1)) and this can be simplified to y = \(\frac{1}{3}x - \frac{1}{6}\) or 2x - 6y - 1 = 0