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Introduction to equations
Solving equations using the index finger method
Solving equations using the balancing method
Writing equations
Solving quadratic equations using the zero product method
Writing equations
Leon is at the gym, working out. He can lift a total of 80 kg. The bar weighs 20 kg. Which expression describes the number (w) of 5 kg weights that he has on the bar when lifting as much as he is able?
Now, when you've learned a bit about equations in general and algebraic expressions in particular, it's time to start writing equations. Prepare a pen and paper, and pause the video when you see this symbol. This way you'll have time to try it yourself before you see the answer. There are four examples in the video. Here's the first one: Maria is at a fruit stand.
She buys 4 apples and 4 mangoes and pays 100 kronor. Write an equation where X represents the amount Maria pays for each of the mangoes. Maria paid 100 kronor in total. We put that on one side of the equals sign. On the other side we write an expression for what she bought: four apples at five kronor each plus four mangoes for X kronor each.
Together they equal 100 kronor. We simplify and tidy up a bit by removing the multiplication sign between four and X. In addition, we usually write the variable term first, so we switch places and get: Four X plus 20 equals a hundred. If you solve this equation for X, you'll know how much is a mango. But for now our goal is just to write an equation.
Let's consider another one: Leon runs a movie club where he shows old horror movies. It costs 200 kronor to become a member. Additionally, tickets cost 40 kronor per movie. Lina has 520 kronor, and she wants to become a member and watch as many movies as she could afford. Write an equation where Y is the number of movies Lina can watch for her money.
Lina has 520 kronor and that should equal the total amount she spends on both the tickets and membership. The tickets cost 40 kronor times Y movies. And membership costs 200 kronor. Two hundred plus forty Y equals 520. If you solve this equation for Y you'll get the number of movies Lina can watch.
Mikael is replacing water in his uncle's aquarium. He knows that he needs 100 liters of water to fill the aquarium and that the aquarium is half a meter deep. He also knows that the aquarium's bottom is 50 centimeters long, but does not know how wide it is. Write an equation where Z is the width of the aquarium's bottom in centimeters. The volume is 100 liters, or 100 000 cubic centimeters.
And the volume of a rectangular prism equals the area of the base times the height. The aquarium is 50 cm deep. And the base is a rectangle with one side of 50 centimeters and the other, Z centimeters. Then you only have to simplify and tidy up, and you will have an equation which, when you solve it, gives you the width of the aquarium in centimeters. Maria is loading sacks of soil into an elevator, which she knows can take exactly 390 kilos before the light flashes and the siren goes off due to overload.
Maria herself weighs 60 kg, and when she loaded 22 sacks the elevator's alarm went off. Write an equation where a sack weighs X kilos. Assume that the load weighed exactly 390 kilos when the alarm went off. Then we have exactly 390 on one side. The other side is Maria's 60 kilos plus 22 sacks of X kilos each.
22 X plus 60 Equals 390. If you solve the equation, you'll find out how many kilos one sack weighs. You watched four examples that showed how to choose numbers and variables in a problem and write down a corresponding equation. Try it yourself with the practice problems. To compose and write a neat equation is a completely different, more creative task than to solve an equation.