Now that students know how to find the amount of a tip, tax or discount using the formula A = p r, it is time for them to solve for p given A and r, or solve for r given A and p.
Preparation Write the equation A = p r on the board. Review what was done yesterday. Review how to solve a multiplication equation such as 3 n = 15.
- Say: Yesterday we used the formula A = p r to solve for A. Today we are going to use this same formula, but instead solve for p or r, whichever is unknown. Who remembers how to solve a multiplication equation like 3 n = 15? (Write 3 n = 15 on the board.)
Students should say we divide both sides by 3, since dividing by 3 is the inverse of multiplying by 3.
- Write the following problem on the board: "A dress that originally sold for $140 is on sale for $84. What is the percent discount?"
- Say: In the problem on the board, what is unknown? (r) What is the original price p? ($140.00) What is the discount amount A? ($56.00)
Students may not know the discount amount. You will need to discuss with students that the discount amount is equal to the original price minus the sales price, or $140 $84 = $56.
- Say: Now, if I substitute these numbers into the equation, what does the equation become? (56 = 140 r) Solve the equation for r at your desks.
The value students will get for r is 0.4. This will need to be changed to a percent, so remind students that 0.4 = 0.40 or forty hundredths, and 40 hundredths is 40%.
- Write this next problem on the board: "A friend is buying your lunch, so you offer to leave the tip. Your friend says OK and tells you to leave $3.60 for the tip. If the standard rate for a tip for lunch is 15%, what was the cost of lunch?"
- Ask: What information do we have given to us?
Students will say that the rate for the tip is 15% and the amount of the tip is $3.60.
- Ask: Who can write the equation for the problem we want to solve? (3.6 = 0.15 p) Try solving this equation at your desk.
- Have a volunteer substitute the numbers into the equation and write the equation on the board. The cost of the lunch, p, was $24. Have the students do similar problems at their desks.
Wrap-Up and Assessment Hints
Getting students to recognize which piece of information is missing in the problems requires them to ask themselves what A, p and r are for each problem. Have them verbalize this information and explain their reasoning.
Point out to students that some problems have more than one step. For example, in problems where they need to find the rate or percent of a discount, the original price and sale price may be given but the amount of the discount is not given. They need to first calculate the amount of the discount before using the formula. In problems where they need to find the sale price of an item, they need to subtract the amount of the discount from the original price after using the formula.