Writing equations to represent problems
Narrator twice says the expressions give the heights 'after two years' when he means after t years. A note in the interventions flags this for students.
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Coral sample A is 8 cm tall and grows 2 cm per year; sample B is 15 cm tall and grows 1.5 cm per year. Sal writes an expression for each height after t years (8 + 2t and 15 + 1.5t) and sets them equal to get an equation for when the heights are the same.
You'll be able to
- write an expression for a quantity that starts at a value and grows by a constant amount each year.
- write an equation showing when two quantities are equal.
- explain what the variable t represents in a real-world equation.
Key words
- variable
- A letter, like t, that stands for a number that can change or is unknown.
- expression
- A maths phrase with numbers, variables and operations but no equals sign, like 8 + 2t.
- equation
- A statement that two expressions are equal, like 8 + 2t = 15 + 1.5t.
- rate
- How much something changes for each unit of time, like 2 cm per year.
Transcript
- [Instructor] We're told A biologist is observing the heights of two coral samples. Sample A is currently eight centimeters tall and grows two centimeters taller every year. Sample B is currently 15 centimeters tall and grows 1.5 centimeters taller every year.
The biologist wants to know how long it will take for their heights to be the same. Let t represent the number of years from now. Write an equation to represent the situation. So like always pause this video, see if you can figure this out and then we can work on this together.
Alright, now let's do it together. So this first statement, it says, sample A is currently eight centimeters tall and grows two centimeters taller every year. How can we write an expression for sample A? Well, it's already eight centimeters tall. We'll just assume all the numbers are in centimeters, and every year it grows two centimeters.
And each year we'll represent t to be the number of years. So the height of sample A is going to be eight plus two times the number of years that have gone by. Fair enough. Now let's think about sample B. It's currently 15 centimeters tall and grows 1.5 centimeters taller every year.
So an expression for the height of sample B after two years would be 15 centimeters plus 1.5 times the number of years that have gone by. Fair enough. Now we want an equation to represent the situation for how long will it take for their heights to be the same, for the heights to be the same.
Well, this is their heights after two years. So we just have to say, well we want these two things to be equal and then solve for t and that will tell us how many years will it take for their heights to be the same and we're done.
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