Question

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

Answer 1

The two numbers in question are -5 and 16, found by setting up a system of equations based on the information provided and using substitution to solve for the variables representing the smaller and larger numbers.

Step-by-step explanation:

The question provides us with two pieces of information about two numbers:

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

Let's denote the smaller number as s and the larger number as l. Now we can translate the given information into two equations:

1. l - s = 21 (since l is larger than s)
2. s + 2l = 27 (the sum of the smaller and twice the larger number)

To solve for the two unknowns, we can use substitution or elimination. Here's a method using substitution:

1. From the first equation: l = s + 21
2. Substitute l in the second equation: s + 2(s + 21) = 27
3. This simplifies to: s + 2s + 42 = 27
4. Combine like terms: 3s + 42 = 27
5. Subtract 42 from both sides: 3s = -15
6. Divide by 3: s = -5
7. Substitute s back into the first equation to find l: l = -5 + 21
8. So l = 16

Therefore, the smaller number is -5 and the larger number is 16.