Section 2.3 The Multiplication Property of Equality 117 Step 2: Read the problem and determine what is given. Use this information to write an equation that models the situation. Step 3: Solve the equation using the addition and multiplication properties of equality. Step 4: Verify that the solution is reasonable. Step 5: Write the answer to the problem and attach appropriate units, if needed. �� ������������������������ ������������������ Write an equation that represents each situation. Solve the equation and explain the answer using a complete sentence. 3a. One less than three times a number is -13. Find the number. Solution 3a. What is known? The number is unknown. Let n represent the number. What is known? One less than three times a number is -13. So, the equation is 3n - 1 = -13 We solve the equation to find the number. 3n - 1=-13 3n - 1 + 1=-13 + 1 Add 1 to each side. 3n=-12 Simplify. 3n 3 = -12 3 Divide each side by 3. n=-4 Simplify. The number is -4. 3b. How many quarters does it take to make $20.00? Solution 3b. What is unknown? The number of quarters is unknown. Let q represent the number of quarters. What is known? The total value of the quarters is $20.00. To find the value of an unknown number of quarters, we use our knowledge of how we calculate the value of a specific number of quarters. Number of Quarters Total Value The total value of a collection of quarters is the value of a single quarter times the number of quarters. 1 (0.25)(1) = $0.25 2 (0.25)(2) = $0.50 3 (0.25)(3) = $0.75 q (0.25)(q) = 0.25q So, to determine how many quarters we need to make $20.00, we can use the equation 0.25q = 20 We solve the equation to find the number of quarters. 0.25q = 20 0.25q 0.25 = 20 0.25 Divide each side by 0.25. q = 80 Simplify. So, it takes 80 quarters to make $20.00. 3c. To rent a moving truck for one day, a company charges $44.95 plus $0.45 per mile. If a family budgets $300 for a moving truck, how many miles will they be able to drive the truck?
hendricks_beginning_algebra_1e_ch1_3
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