The sum of two numbers is 95. If the larger number is increased by twice the smaller number, the result is 120. What is the larger number?
If x = the smaller number and y = the larger number, then which of the following systems of equations represents the word problem?
x + y = 95 and x + 2y = 120
x + y = 95 and 2x + y = 120
x + y = 95 and 2(x + y) = 120

Question

The sum of two numbers is 95. If the larger number is increased by twice the smaller number, the result is 120. What is the larger number?
If x = the smaller number and y = the larger number, then which of the following systems of equations represents the word problem?
x + y = 95 and x + 2y = 120
x + y = 95 and 2x + y = 120
x + y = 95 and 2(x + y) = 120

anonymous · Answer

The first one is the correct option. The sum of the numbers is 95, which can be expressed by the equation x + y = 95.
Twice the second number is 2y. So the larger number increased by twice the smaller number means x + 2y and their sum is  120.