SUBSTITUTION WORD PROBLEMS

On this webpage substitution word problems we are going to see how to solve a word problem using substitution method.

Formulate the following problems as a pair of equations,and hence find their solutions:

(i) One number is greater than thrice the other number by 2. If 4times the smaller number exceeds the greater by 5, find the numbers.

Solution:

Let “x” be one number and “y “ be another number

Here one number is defined by other number

                x = 3 y + 2  ----- (1)

Here we have two variables x and y. In these two terms x is greater number and y is smaller number

                 4y = x + 5   ----- (2)

Substitute (11) in the second equation we get

            4 y = 3y + 2  + 5

           4 y - 3 y = 7

                      y = 7

Now we need to apply the value of y in first or second equation to get the value of y.

Substitute y = 7 in the first equation

              x = 3(7) + 2

              x = 21 + 2

              x = 23

Therefore one number is 23 and other number is  7.

Verification:

x = 23       y = 7

23 = 3 (7) + 2

23 = 21 + 2

23 = 23


(ii) The ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.If each of them manages to save $2000 per month, find their monthly income.

Solution:

Let 9x and 7 x be the income of two persons

Let 4y and 3 are the expenditure of two persons

Each of them manages to save $2000.

Income – expenditure = savings

         9 x – 4 y = 2000  ----- (1)

         7 x – 3 y = 2000  ----- (2)

Multiply the first equation by 3 we get

                       27 x – 12 y = 6000 ----- (3)

Multiply the first equation by 4 we get

                       28 x – 12 y = 8000  ----- (4)

                       27 x – 12 y = 6000

                       28 x – 12 y = 8000

                        (-)      (+)          (-)

                     ---------------------------

                         -x   = -2000

                          x = 2000

Substitute x = 2000 in the first equation we get

9 (2000) – 4 y = 2000

 18000 – 4 y = 2000

               -4y = 2000-18000

              -4y= - 16000

                  y = 4000

Monthly income of first person = 9 x = 9 (2000) = 18000

Monthly income of second person = 7 x = 7 (2000) = 14000      

Verification:

9 x – 4 y = 2000 

9(18000) - 4(4000) = 2000

162000-16000 = 2000

2000 = 2000

Try other questions

(ii) The ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.If each of them manages to save $2000 per month, find their monthly income.  Solution

(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.  Solution

(iv) Three chairs and two tables cost $700 and five chairs and three tables cost $1100.What is the total cost of 2 chairs and 3 tables.  Solution

(v) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm ². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle.   Solution

(vi) A train traveled a certain distance at a uniform speed. If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time. If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train. Solution

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