Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

Question

2 y + x = 5. 5 x minus y = 3.
2 x + y = 5. 5 y minus x = 3.
2 y + x = 5. y minus 5 x = 3.
2 x + y = 5. x minus 5 y = 3.

Answer 1

Let's review the problem step by step to derive the correct equations.

1. Twice a number added to a smaller number is 5:

   • Let \( x \) be the smaller number and \( y \) be the larger number.
   • Twice the larger number added to the smaller number can be written as: \[ 2y + x = 5 \]

2. The difference of 5 times the smaller number and the larger number is 3:

   • This can be expressed as: \[ 5x - y = 3 \]

Combining both of these, we get the two equations:

• \( 2y + x = 5 \)
• \( 5x - y = 3 \)

So, the correct representation of the situation is: 2y + x = 5. 5x - y = 3.

Therefore, the answer is: 2y + x = 5. 5x - y = 3.