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Section 2.7 Consecutive Integers Consecutive integers are integers that are next to each other on the number line For example: 5 and 6 13 and 14 –4 and –3. Consecutive odd integers are odd integers that follow one another on the number line. For example: 3 and 5 11 and 13 –9 and –7. Translating words to algebraic statements. The sum of two consecutive odd integers is 28. Find the two integers. Step 1: Understand: Known items: Numbers are integers They are consecutive and odd Adding them gives a total of 28. Find: Both numbers Step 2: Plan Let x = the first consecutive odd integer Always start with a Let Statement Then x + 2 is the next consecutive odd integer x + (x + 2) = 28 Create an equation Step 3: Carry Out x + (x + 2) = 28 2x + 2 = 28 2x = 26 x = 13 and (13) + 2 = 15 Simplify the left side Add –2 to each side Multiply each side by Step 6: Check. Suppose the first odd integer is 13. The next consecutive odd integer is 15. The sum of 15 and 13 is 28. Answer: 13 and 15 Interest You invest money in a bank account (or CD). The account earns 8% in annual interest. You invest the same amount plus an additional $2,000 in a second account. This account earns 9% in annual interest. At the end of the year, the total interest earned in both accounts is $690. How much did you invest in each account? Step 1: Understand Known items: The interest rates (8% and 9%) The total interest earned ($690) Investment at 9% is $2,000 more than investment at 8% Find: The amount invested at 8% The amount invested at 9% Step 2: Plan Let x = the amount of money invested at 8%. Then, x + 2,000 = the amount of money invested at 9%. The interest earned on x dollars invested at 8% is 0.08x. The interest earned on (x + 2,000) dollars invested at 9% is 0.09(x + 2,000). Step 2: Plan Let’s summarize this information in a table: Because the total amount of interest earned from both accounts is $690, the equation that describes the situation is: Interest earned + Interest earned = Total interest at 8% at 9% earned 0.08x + 0.09(x + 2,000) = 690 Step 3: Carry Out 0.08x + 0.09(x + 2,000) = 690 0.08x + 0.09x + 180 = 690 0.17x + 180 = 690 0.17x = 510 Distributive property Add 0.08x and 0.09x Add –180 to each side Divide each side by 0.17 x = 3,000 (at 8%) and (3,000) + 2,000 = 5,000 (at 9%) Step 4: Check The interest at 8% is 8% of 3,000 or 0.08(3,000) = $240 The interest at 9% is 9% of 5,000 or 0.09(5,000) = $450 The total interest is $690 Triangles One angle of a triangle is twice the smallest angle. The other angle is three times as large as the smallest angle. Find the measure of all three angles. Step 1: Understand Known items: The sum of the angles in a triangle is 180° One angle is twice the smallest angle The largest angle is three times the smallest angle. Find: The measure of all three angles Step 2: Plan Draw a triangle Label the smallest angle as x, then 2x will be the measure of another angle and 3x will be the measure of the largest angle. Step 2: Plan Let Statement Let x = the measure of the smallest angle Then, 2x = the measure of the second angle and 3x = the measure of the third angle. x + 2x + 3x = 180° Equation Step 3: Carry Out x + 2x + 3x = 180° 6x = 180° x = 30° and 2(30°) = 60° 3(30°) = 90° Step 4: Check. The angles must add to 180°: 30° + 60° + 90° ≟ 180° 180° = 180° Answer: 30°, 60°, 90° Our answers check Section 2.7 Page 179-184 # 1, 9, 15, 17, 21, 23 Please bring graph paper, a ruler and a pencil for the next class.