Twice a number plus twice a second number is 310. the difference between the numbers is 55. find the numbers by writing and solving a systrm of equations.

The numbers are 105 and 50

Solution:

Let "x" be the first number

Let "y' be the second number

Twice a number plus twice a second number is 310

Therefore,

twice of x + twice of y = 310

2x + 2y = 310 eqn 1

The difference between the numbers is 55

x - y = 55 eqn 2

Let us solve eqn 1 and eqn 2

From eqn 2,

x = 55 + y eqn 3

Substitute eqn 3 in eqn 1

2(55 + y) + 2y = 310

110 + 2y + 2y = 310

4y = 310 - 110

4y = 200

Substitute y = 50 in eqn 3

x = 55 + 50

Thus the numbers are 105 and 50

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