Question

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.

Answer 1

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

y = 50

Substitute y = 50 in eqn 3

x = 55 + 50

x = 105

Thus the numbers are 105 and 50