Question

The sum of two numbers is 105. If the larger number is increased by twice the smaller number, the result is 138. What is the larger number? If x is the smaller number and y is the larger number, which of the following system of equations represents the word problem?

x+y=105

x+2y=138


x-y=105

y+2x=138


x+y=105

y+2x=138

Answer 1

The last set of equations is correct:
x + y = 105
y + 2x = 138

Subtract the top equation from the bottom equation to cancel out y:
2x - x = 138 - 105
x = 33
Plug value of x into top equation:
33 + y = 105
y = 105 - 33
y = 72
So the larger number is 72.