simple equations STD V

• If you subtract ½ from a number and multiply the result by ½, you get 1/8. What is the Number?  

         Answer:

          Let the number be y

          Then, (y- ½ ) x ½ = 1/8

          Or, y – ½ = 2/8 = ¼

          Or, y = ½ + ¼ = ¾ 

• The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15cm. What is the length of either of the remaining equal sides?

          Answer

          Let the side be y.

          Since it is an isosceles triangle, the 2 sides are equal.

          So, the equation would be y + y + 4/3 = 4 ²/₁₅ = 62/15

          Or, 2y = 62/15 – 4/3

          Or, 2y = (62 – 20)/15

          Or, 2y = 42/15

          Or, y = 42 / (15 x 2) = 21/15 = 1 ⁶/₁₅

• The sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

         Answer:

         Let one of the number be y.

         Then the other number is y + 15.

         Given that y + y + 15 = 95

         Or, 2y + 15 = 95

         Or, 2y = 95 -15

         Or, 2y = 80

         Or, y = 40

         Therefore the other number is y + 15 = 40 + 15 = 55.

         The two numbers are 40 and 55.

• Two numbers are in the ration of 5:3. If they differ by 18, what are the numbers?

         Answer

         Let one of the number be y.

         The other number is y-18

         We are given that y: y-18 = 5:3

         Product of mean = product of extreme.

         So, 3y = 5(y-18)

         Or, 3y = 5y -90

         Or, 2y = 90

         Or, y = 45

         Therefore, y -18 = 27

         So, the 2 numbers are 27 and 45.