Answer to Question #34512 in Algebra for alan

Question

the sum of two numbers is 117 seven time one number plus three times the other is 623. Find the numbers

Answer 1

Let x and y be unknown numbers. Then we have the system of 2 equations:
x + y = 117
7x + 3y = 623

Let's solve the system.
From the first equation x = 117 - y. Now substitute it into the second one:
7(117-y) + 3y = 819 - 4y = 623
4y = 819 - 623 = 196
y = 196 / 4 = 49
x = 117 - 49 = 68

So the two numbers are 68 and 49.