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In this video we look at how to derive equations and expressions from sentences. We can write ‘c’ minus 5 in symbols rather than words: c - 5. And d times 4: 4d. But we can do much more than this. We can actually turn sentences into algebra, to help us solve different problems. Like if we have this information: "1 cup of coffee costs $2.20. Write down an expression for the cost of x cups of coffee." So if we wanted to buy ‘x’ number of cups, we multiply 2.20 by x. And in algebra, we remove the multiplication sign so it's 2.20x. Then if we wanted 100 cups, we’d replace the x with 100. 100 cups = 2.20 X 100 = £220. We can also write multiple sentences into expressions and solve equations from these expressions. "Adult tickets = £12, Child tickets = £8. Write down an expression for the cost of x adult tickets and y child tickets." From this, for adults tickets the expression is 12x where x is the number of adults. And for children the expression is 8y where y is the number of children. An expression for the total cost of tickets would be 12x + 8y. We can even have 3 or more statements involved: "Andrew is x years old, David is 8 years older than Andrew and Jane is twice as old as Andrew. The total of their ages is 88." From this, we can say that Andrew is x, David is x+8 and Jane is 2x. As the total of their ages is 88, we can write an equation: Andrew + David + Jane = 88, and then replace the people with the expressions: x + x+8 + 2x = 88. And solve this equation: 4x+8=88. 4x=80. x=20.

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