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?
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.
