Question

The difference between one number and a smaller number is 21. The sum of the smaller and twice the larger is 27.

Answer 1

To solve this problem, we set up a system of equations and solve for the values of x and y. The larger number is 16 and the smaller number is -5.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume the larger number is x and the smaller number is y. According to the given information, we have the following equations:

1) x - y = 21

2) y + 2x = 27

From equation 1, we can express x in terms of y: x = y + 21. Substituting this into equation 2, we get: y + 2(y + 21) = 27. Simplifying, we have 3y + 42 = 27. Subtracting 42 from both sides, we get 3y = -15. Dividing by 3, we find y = -5.

Substituting this value back into x = y + 21, we get x = -5 + 21 = 16. Therefore, the larger number is 16 and the smaller number is -5.