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If 2w + 4t = 14 and 4w + 5t = 25, what i...

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

A

6

B

10

C

13

D

17

Text Solution

Verified by Experts

The correct Answer is:
C
Multiplying both sides of 2w + 4t = 14 by 2 yields 4w + 8t = 28. Subtracting the second given equation from 4w + 8t = 28 yields (4w − 4w) + (8t − 5t) = (28 − 25) or 3t = 3. Dividing both sides of this equation by 3 yields t = 1. Substituting 1 for t in the equation 2w + 4t = 14 yields 2w + 4(1) = 14, or 2w + 4 = 14. Subtracting 4 from both sides of this equation yields 2w = 10, and dividing both sides of this equation by 2 yields w = 5. Substituting 5 for w and 1 for t in the expression 2w + 3t yields 2(5) + 3(1) = 13.
Choices A, B, and D are incorrect and may result from incorrectly calculating the values of w and t, or from correctly calculating the values of w and t but finding the value of an expression other than 2w + 3t. For instance, choice A is the value of w + t, choice B is the value of 2w, and choice D is the value of 2t + 3w.
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