If 2w + 4t = 14 and 4w + 5t = 25, what is the value of 2w +3t?

Explanation

The correct answer is 13. To solve the system, multiply the first equation, 2w + 4t = 14, by 2 to obtain 4w + 8t = 28. Subtract the second equation, 4w + 5t = 25, from this new equation to eliminate w: (4w - 4w) + (8t - 5t) = (28 - 25), resulting in 3t = 3. Solving for t gives t = 1. Substitute t = 1 into the first equation to find w: 2w + 4(1) = 14 simplifies to 2w = 10, so w = 5. Substituting w = 5 and t = 1 into 2w + 3t results in 2(5) + 3(1) = 13. The other options result from incorrectly calculating or misinterpreting the given expressions.