Question

The larger of two numbers is 14 more than twice the smaller number. Find the numbers if their sum is 80.

a) 33 and 47
b) 36 and 44
c) 28 and 52
d) 40 and 40

Answer 1

To find two numbers where one is 14 more than twice the other and their sum is 80, we set up equations and solved for the smaller number, which is 22, and the larger, which is 58. The correct pair of numbers is not listed in the provided options.

Step-by-step explanation:

The question states that the larger of two numbers is 14 more than twice the smaller number and their sum is 80. We can set up two equations to represent this information:

1. Let x be the smaller number.
2. Then, the larger number is 2x + 14.
3. The sum of the two numbers is x + (2x + 14) = 80.
4. Simplifying the sum equation gives us 3x + 14 = 80.
5. Subtracting 14 from both sides gives us 3x = 66.
6. Dividing both sides by 3 gives us x = 22.

Therefore, the smaller number is 22, and the larger number is 2(22) + 14 = 58.

Since none of the answer choices match our result of 22 and 58, we need to look back at the calculations. If the calculations are correct, the student must be informed that the correct pair of numbers is not listed in the options.