The sum of two numbers is 15. Four times the smaller number is 60 less than twice the larger number. What is the larger number?
I need to find two numbers that add up to 15 and satisfy another condition involving their multiples. Let me call the smaller number x and the larger number y, so I have x + y = 15 and 4x = 2y - 60. I can try to solve this system of equations by substitution or elimination. Substitution might be easier, since I can easily isolate x or y from the first equation. If I solve for y, I get y = 15 - x, and then I can plug that into the second equation. So I have 4x = 2(15 - x) - 60, which simplifies to 4x = 30 - 2x - 60, and then to 6x = -30. Dividing both sides by 6, I get x = -5. That means the smaller number is -5, and the larger number is 15 - (-5) = 20. I can check my answer by plugging it back into the original equations. Indeed, -5 + 20 = 15 and 4(-5) = 2(20) - 60, so I'm confident that I found the correct numbers. 