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