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...

Answer Details

a) Let's assume that one boy consumes x kilograms of rice per day. Then, we can write the equation as follows:

10mx = 20 (since m boys consume the rice in 10 days)

(10m+4)(x) = 20 (since 4 more boys joined and the same amount of rice lasted for 8 days)

Simplifying the equations, we get:

mx = 2

(10m+4)(x) = 2(10m)(8)

Dividing the second equation by the first equation, we get:

10m+4 = 4(80)

10m = 316

m = 31.6

Since the number of boys has to be a whole number, we can round up to m=32.

b) Let's assume that the number is represented by n. Then, we can write the equation as follows:

\(\frac{5}{6}\)n = \(\frac{1}{3}\)n + 10

Multiplying both sides by 6 to eliminate the fractions, we get:

5n = 2n + 60

3n = 60

n = 20

c) We can find the equation of the line passing through two points using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points given.

m = (-1/2 - 1/2) / (-1 - 2) = -1/3

Now, we can use either of the two points to find the y-intercept. Let's use (2, 1/2):

1/2 = (-1/3)(2) + b

b = 5/6

Therefore, the equation of the line is y = (-1/3)x + 5/6.