Sum of a larger number and twice of a smaller number is 87 . Find them if their difference is 36.

Question

Hi, the question deals with systems of linear equations

Answer 1

Hello Kyle,

 

I always use x  and y...

Let x = large number 

Let y = small number

 

I will go back to the problem..Then, I will formulate an equation based on the given sentence of the problem...

 

So, I have    x  +  2y   = 87  ( sum of the larger (x) and twice the smaller (y) is 87

                   x  -     y    = 36   their difference is 36

 

Using elimination by subtraction , my new set of equations are   x  +  2y  = 87

                                                                                                - x   +  y   = - 36  ( Change the sign of subtrahend ...)

                                                                                              __________________

                                                                                                           3y  = 51

                                                                                                             y   = 17

Thus, the smaller number y = 17 

To get the larger,  x - 17 = 36

                                     x = 53

          To check:

       x   +  2y  = 87

       53  +  2 (17)  = 87

        53  +  34  = 87

 

        

 

Answer 2

Hi Kyle,

 

Let L = larger number, S = smaller then write equations based on the words that are provided.

 

1. L + 2S = 87 [sum (+) of larger and twice smaller (2S) is (=) 87]

2. L -    S = 36 [difference (-) is (=) 36]

 

Now you have two equations with two unknowns. Use substitution or elimination method to solve.

Substitution:

Solve #2 for L. L = S + 36

Substitute that value for L in equation #1:

(S +36) + 2S = 87

3S = 87-36 (51)

S = 51/3 = 17

L = 17 + 36 = 53