Writing and Solving Two-Step Equations

We are asked to write an equation that represents the bicycle's original price. First, let's represent the unknown quantity with a variable. Here, the unknown quantity is the bike's original price p. On sale, the bike is 20 % off, or in other words 15 cheaper. Then, the price of the bike on sale is p- 15 p, or 45p. 4/5p = Bicycle Sale's Price In addition, Kriz has a coupon. They can pay $50 less than the sales price of the bicycle. 4/5p - 50 = Price Kriz Pays We know that Kriz only needs to pay $350 for the bike. This lets us complete the equation. 4/5p - 50 = 350 This equation can help us find the original price of the bike. Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be obtained by applying the Properties of Equality to the above equation.

We want to write an equation that represents the given situation. We first represent the unknown quantity with a variable. Here, the unknown quantity is the original number of birds. We will call it b. We know that half of the birds stayed. Then, the number of birds that stayed on the power line is 12 b. 12 b = Number of Birds That Stayed on the Power Line After that, 4 more birds sat on the power line. The final number of the birds on the power line was 12b + 4. 12 b + 4 = Final Number of Birds on the Power Line We know that in the end, there were 10 birds on the power line. This lets us complete our equation. 12 b + 4 = 10 This equation can help us find the number of birds that were sitting on the power line in the beginning. Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be obtained by applying the Properties of Equality to the above equation.

We want to write an equation that represents the given situation. First, let's represent the unknown quantity with a variable. Here, the unknown quantity is the original price of the shoes. We will call it p. We know that the shoes are 50 % off. Then, the price of the shoes on sale is 12 p. 12 p = Shoe's Sales Price We know that Tearrik paid $45 less than the regular price of the shoes. This means that the price of the shoes on sale is equal to p- 45 . This lets us complete the equation. 1/2p = p- 45 This equation can help us find the original price of the shoes. Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be obtained by applying the Properties of Equality to the above equation.

We want to write an equation that represents the given situation. We first represent the unknown quantity with a variable. Here, the unknown quantity is the original time it took Vincenzo to run 100 yards. We will call it t. t = Vincenzo's time before he started training We know that Vincenzo improved his time by a sixth. In other words, his time after training is 56 his time before the training, or 56 t. 56 t = Vincenzo's time after training We also know that Vincenzo's improved time is 2 seconds faster than his original time. This tells us that it can be expressed as t - 2. Now we can write an equation. 56 t = t - 2 This equation can help us find Vincenzo's time before he started training. Note that we can write different equations, but they will all be equivalent to the equation we wrote. These equivalent equations can also be obtained by applying the Properties of Equality to the above equation.