Q3 of 71 Page 65

The sum of two numbers is 70 and their difference is 6. Find these numbers by cross – multiplication method.

Let the two numbers be x and y.


According to the question,


x + y = 70 and x – y = 6


⇒ x + y – 70 = 0 and x –y – 6 = 0


On comparing with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0we get,


a1 = 1, b1 = 1, c1 = – 70; a2 = 1, b2 = – 1, c2 = – 6


Applying cross multiplication method which says,



Putting the given values in the above equation we get,






Similarly,



∴The solution of the pair of equations is (38, 32).


So, the required numbers will be 38 and 32.


More from this chapter

All 71 →
1

Solve the following pairs of equations by cross multiplication method:

3x + y = 5, 5x + 3y = 3

 2

By cross multiplication method, find such a two digit number such that, the digit at unit's place is twice the digit at tens place and the number obtained by interchanging the digits of the number is 36 more than the original number.

 4

While arranging certain students of a school in rows containing equal number of students; if three rows are reduced, then three more students have to be arranged in each of the remaining rows. If three more rows are formed, then two students have to be taken off from each previously arranged rows. Find the number of students arranged.

 5

In AABC, the measure of ∠B is thrice to the measure of ∠C and the measure of ∠A is the sum of the measures of ∠B and ∠C. Find the measures of all the angles of AABC and also state the type of this triangle.