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Question
The average of a, b, c is 6 and a - b = 4 , ab = 21, What is the value of c?
6
7
8
9
ANSWER : 3
Descrption
<p style="margin-left:0px;">We are given:</p><p style="margin-left:0px;">The average of a, b, and c is 6: (a + b + c) / 3 = 6</p><p style="margin-left:0px;">a - b = 4</p><p style="margin-left:0px;">ab = 21</p><p style="margin-left:0px;">Let's use these equations to solve for c. First, we can find the values of a and b:</p><p style="margin-left:0px;">From the equation a - b = 4, we can express a in terms of b: a = b + 4.</p><p style="margin-left:0px;">Now, we can substitute this expression for a into the equation ab = 21:</p><p style="margin-left:0px;">(b + 4)b = 21</p><p style="margin-left:0px;">Expand and simplify:</p><p style="margin-left:0px;">b^2 + 4b = 21</p><p style="margin-left:0px;">Subtract 21 from both sides:</p><p style="margin-left:0px;">b^2 + 4b - 21 = 0</p><p style="margin-left:0px;">Now, let's solve this quadratic equation for b. We can factor it:</p><p style="margin-left:0px;">(b + 7)(b - 3) = 0</p><p style="margin-left:0px;">Setting each factor equal to zero gives us two possible values for b:</p><ol><li>b + 7 = 0 → b = -7</li><li>b - 3 = 0 → b = 3</li></ol><p style="margin-left:0px;">Now that we have the values of b, we can find a using the equation a = b + 4:</p><ol><li>For b = -7, a = -7 + 4 = -3</li><li>For b = 3, a = 3 + 4 = 7</li></ol><p style="margin-left:0px;">Now, we can find c using the average equation:</p><p style="margin-left:0px;">(a + b + c) / 3 = 6</p><p style="margin-left:0px;">We have two sets of values for a and b, so we'll find two possible values for c:</p><ol><li>For a = -3 and b = -7:</li></ol><p style="margin-left:0px;">((-3) + (-7) + c) / 3 = 6 (-10 + c) / 3 = 6</p><p style="margin-left:0px;">Multiply both sides by 3:</p><p style="margin-left:0px;">-10 + c = 18</p><p style="margin-left:0px;">Add 10 to both sides:</p><p style="margin-left:0px;">c = 18 + 10 c = 28</p><ol><li>For a = 7 and b = 3:</li></ol><p style="margin-left:0px;">((7) + (3) + c) / 3 = 6 (10 + c) / 3 = 6</p><p style="margin-left:0px;">Multiply both sides by 3:</p><p style="margin-left:0px;">10 + c = 18</p><p style="margin-left:0px;">Subtract 10 from both sides:</p><p style="margin-left:0px;">c = 18 - 10 c = 8</p><p style="margin-left:0px;">So, we have two possible values for c: c = 28 or c = 8.</p>
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