Topic A: Use properties of operations to generate equivalent expressions
Martin likes to make flower bouquets that each have 3 violets and 4 tulips. If the price of a violet is V and the price of a tulip is T, match the expressions to their meanings. So let's see-- the price of 1 of Martin's bouquets. So one of Martin's bouquets has 3 violets and 4 tulips. So the 3 violets are going to cost 3 times the price of the violet, which is V. So that's the cost of the violets, 3V. And then the 4 tulips are going to cost 4 times the price of a tulip. So that's 4T. So it's 3V plus 4T. So it's not this one. Let's see. This one right over here, this is 4T plus 3V. So this is the price of 4 tulips, 4 times the price of a tulip, plus 3 times the price of a violet. The price of 3 of Martin's bouquets, so it's essentially going to be 3 times this quantity right over here. This is the price of 1 bouquet. We want 3 of them. So it's going to be 3 times the quantity 4T plus 3V. And let's see. If I were to actually multiply this out, 3 times 4T is 12T, and then plus 3 times 3V is 9V. So this is the same thing if I were to distribute the 3-- is 12T plus 9V. Well, that's this right over here. These two are equivalent expressions. And let's see. Are any of these other things equivalent? No, this says 3 times 3T plus 4V. So I'm going to put this in the not used bucket. And then I have-- let's see-- 3V plus 2T. I'm going to put it in the not used bucket. And let's see. This has 2V plus 4T plus V. So if I were to simplify this, if I were to combine the V terms-- if I have two V's and I add another V, that's three V's plus 4T. So this is actually the same thing as the price of 1 of Martin's bouquets. So you could view this as the price of 2 violets plus the price of 4 tulips plus another violet. So it's really the price of 3 violets and 4 tulips. So let's check our answer. We got it right.