To get the total cost of t tables and c chairs, we must multiply each of these counts of items by the cost per item (and then add the two costs):
cost = 51t + 34c
We have an expression for the cost, but it doesn't match any of the answer choices. However, there is a common factor of these two terms: 17. If that fact is not immediately clear, you can determine it by looking at the answer choices and testing: 17 × 2 = 34 and 17 × 3 = 51. Factoring out 17 from our original equation, we get:
cost = 17(3t + 2c)
Another way to match our expression with the answer choices would be to expand the answer choices by multiplying out the parentheses. It's the same mathematical operation as factoring, but in the other direction. When we get to choice (D) and multiply it out, we get:
17(3t + 2c) = 17(3)t + 17(2)c = 51t + 34c.