In a two-digit number, the tens digit is two less than the units digit. if the digits are reversed, the sum of the reversed number and the original number is 154. find the original number.

Denote the number by , where are positive integers between 0 and 9 .

"the tens digit is two less than the units digit"

Reversing digits gives a new number .

"sum of the reversed number and the original number is 154"

Simplify the second equation:

Since , by substitution we get

which in turn gives

So the original number is .

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

47 - 90 = 43

43 - 180 = x

x = 137