Question

A number consists two digits whose sum is 8. If 18 is added to the number its digits are reversed. Find the number.
2) Two equal sides of a triangle are each 5 metres less than twice the third side. If the perimeter of the triangle is 55 metres, find the lengths of its sides.

Answer 1

1) stuck...think of a number example, eg 27. What does this mean?

it means (2x10) + 7.

ok, so our number is xy, which means 10x+y.

Anyway, the first sentence say the sum of the 2 digits is 8, so x+y = 8

if we add 18 to the number, ie 10x+y+18 the result is then yx (ie 10y+x)
--> 10x+y+18 = 10y+x
--> 9x + y + 18 = 10y
--> 9x - 9y + 18 = 0
--> 9x - 9y = -18
--> x - y = -2

So we have 2 equations:
x+y=8
x-y=-2

solve these to give x=3 and y=5 ie we had 35 and 53.



2)Let the length of third side be a units

length of equal sides = (2a -5) units

now, perimeter = 55
⇒a + (2a-5) +(2a-5) = 55
⇒5a =65
⇒a =13

2a-5=21, other two side

so length of sides are 13 m, 21 m and 21 m