**Video Transcript**

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Transcript
**Understanding Equations**

Phineas Fogg has just received an exclusive advertisement for the new trans-Siberian railway. He thinks that he can now complete a trip around the world in just 80 days! He’s so confident, in fact, that he makes a bet with his buddies. In order to plan his trip, Phineas will need to understand expressions and equations. Phineas wants the total length of the trip to be 79 days, you know, just in case something goes awry. He'd like to take trains and steamers as his primary modes of transportation. Over land, he’ll take trains. Over sea, he’ll take steamers. It’d be silly to do it the other way 'round. He figures that there will be 5 legs of his trip by train. Two of the legs will be exactly 13 days long, two more will be 7 days long and one leg will be a whopping 22 days long! If the rest of the trip is to be done by steamer, how many days does Phineas have left? We know that Phineas wants his trip to last 79 days, so we can simply subtract the number of days he plans to travel by train from 79, giving us the number of days he's able to travel by steamer. Now, we need to calculate the total number of days Phineas Fogg plans to travel by train. To do this, we have to add the duration, in days, for each of the 5 legs of the trip he plans to travel by train. There are two legs that are 13 days long, as well as two legs that are 7 days long. We can multiply 13 and 7 by 2, since each duration occurs twice. The final leg of the trip by train is the longest at 22 days, so we just add that to find our grand total. We can substitute this into our original equation and then solve. Remember! You have to distribute the negative sign to all the terms in the parentheses. Now, just complete the process by using PEMDAS. Remember to solve from left to right, and we have our answer! 17 Days. Now that we know how long the trip should take, we should probably help Phineas figure out how much the trip'll cost since no one’s made of money. We need to know how many of each kind of ticket Phineas needs to purchase, as well as the cost of the different modes of transportation. If each train ticket costs two-thirds the price of a steamer ticket... We can represent the train ticket price in terms of the steamer ticket price. Each steamer ticket will cost 45 pounds, so we can substitute this value here and here. Phineas will need 5 train tickets and 3 steamer tickets. Let's evaluate what we have. 3 times 45 is 135. 5 times two-thirds is 10 over 3. 10 over 3 times 45 is 150, and 135 plus 150 gives us our grand total and how much money Phineas needs for the tickets: 285 pounds sterling. Satisfied that he'll have the funds and the time to make it around the world in 80 days, Phineas sets off on his journey. Let's check on his progress.

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Solve Problems Using Expressions, Equations, and Inequalities (3 Videos)

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