simple equations STD V

• Three Consecutive integers add up to 51. What are these integers?

          Let the integers be y-1, y, y +1.

         Given that y-1 + y + y +1 = 51

         Or, 3y = 51

         Or, y = 17

         So, the three numbers are 16, 17 and 18.

• The sum of 3 consecutive multiples of 8 is 888. Find the multiples?

          Let the numbers be y-8, y and y +8

         Given that y-8 + y + y + 8 = 888

         Or, 3y = 888

         Or, y = 296

         So, the three numbers are 288, 296, 304

• The ages of Rahul and Haroon are in the ratio of 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

         Let the age of Rahul four years hence be y.

         So, age of Haroon is 56 – y.

         Present age of Rahul = y – 4

         Present age of Haroon = 56 – y – 4 = 52 – y

        Given y-4 : 52 – y = 5 : 7

         The product of mean = product of extreme. So,

         7(y – 4 ) =5(52 – y)

        Or, 7y – 28 = 260 – 5y

        Or, 12y = 260 + 28 = 288

        Or, y = 288/ 12 = 24

        So, Haroon’s age 4 years hence is = 56 – y = 32

        So, the present age of Rahul and Haroon are = 20 and 28.

• The number of boys and girls in a class are in the ratio of 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

          Answer:

          Let the number of girls in the class be y

          So, the number of boys = y + 8

          Given that, (y+8):y = 7:5

          Product of mean = product of extreme, so,

          5(y+8) = 7y

         Or, 5y + 40 = 7y

         Or, 2y = 40

         Or, y = 20

         So, the total strength of the class is = y + y+8 = 20 + 28 = 48.