Question

a number exceeds another by 7 . if 2 is added to the greater number the sum is three times the difference if 5 is subtracted from the smaller. find the greater number

Answer 1

Let the two numbers be a , b

a - b = 7 => (1st equation)

(2+a) + (b-5) = 7 * 3

2 + a + b - 5 = 21

2 + a + b = 26

a + b = 24 => (2nd equation)

From 1 and 2, we solve the two equations together either with or without the calculator

If you're not using the calculator
You do this:

a - b = 7
a + b = 24 Since b is positive in one equation and negative in the other we don't have to change all the signs in one equation, so we cancel b with -b and sum up the rest of the two equations

a + a = 24 + 7
2a = 31
a = 15.5

We go back to one of the equations (whichever one you like) so as to know b equals what. But in that question you don't need the b since the a is the larger number.
But i'll show you how to get it anyways

a + b = 24
15.5 + b = 24
b = 8.5

If you're using the calculator:
You click on mode , equation , 1 , you're looking for the one that's gonna require two equations to be written
And you write the cofficient of the letters a and b , aka the number besides them which is in this case 1. If the equation goes like this : 2a + 3b = 18 then on the calculator you type 2 , 3 and 18

Answer 2

Answer:

Step-by-step explanation:

As per the given data, Let the small number be 'x' and the large number be 'x + 7'

                         (i.e.) (x + 7) + 2 = 3 (x - 5)

                                 x + 9 = 3x - 15

                                3x - x = 15 + 9

                                 2x = 24               x = 242

                             Ans: x = 12            (i.e.) small number = 12 & large number = 19