Writing Algebraic Expressions for Picture Problems

Hi, welcome to this video lesson for creating an algebraic equation for a diagram. Let’s jump right into it, shall we? The scale below is balanced. The small blocks each weight two pounds. The large blocks each way p pounds. Find the weight of the large blocks. Since both sides are equal, we can feel comfortable using an equals sign to show the relationship between the two.

It looks like the left side has 9 small boxes and the right side has two big boxes and three small boxes. If those items are equal to one another, then we can create an equation that looks like this: 9 small boxes = 2 big boxes + 3 small boxes, or 9s = 2b + 3s, where S is for small and B is for big. We also know that small boxes are two pounds each. If, therefore, we want to solve for the weight of a big box, we can rewrite our equation like this: 9s = 2b + 3s. Then, 6s = 2b, because we can subtract 3s from both sides.

Whatever we do to one side, we must do to the other. 3s = 1b, because we can divide both sides by 2. We now know S is equal to 2 pounds. Let’s substitute it in. That gives us six pounds = one big box. There we go. We have her answer. Thanks for watching this video lesson. Until next time, happy studying.