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

Question

Mathematics

Brenden Barber

4 December, 03:25

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

+4

Answers (1)

Know the Answer?

Marcus Arias · 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.