2006
Mathematics
67ca00ce0c643c71d77dee1f
If the mean of five consecutive integers is 30, find the largest of the numbers
A.
28
B.
30
C.
32
D.
34
Correct Answer: 32
Explanation
Solution: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mi>a</mi>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>1</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>2</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>3</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>5</mn>
</mfrac>
<mspace linebreak="newline"></mspace>
<mn>30</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5</mn>
<mi>a</mi>
<mo>+</mo>
<mn>10</mn>
</mrow>
<mn>5</mn>
</mfrac>
<mspace linebreak="newline"></mspace>
<mn>30</mn>
<mo>×</mo>
<mn>5</mn>
<mo>=</mo>
<mn>5</mn>
<mi>a</mi>
<mo>+</mo>
<mn>10</mn>
<mspace linebreak="newline"></mspace>
<mn>5</mn>
<mi>a</mi>
<mo>=</mo>
<mn>150</mn>
<mo>−</mo>
<mn>10</mn>
<mspace linebreak="newline"></mspace>
<mn>5</mn>
<mi>a</mi>
<mo>=</mo>
<mn>140</mn>
<mspace linebreak="newline"></mspace>
<mi>a</mi>
<mo>=</mo>
<mn>28</mn>
<mspace linebreak="newline"></mspace>
<mo>∴</mo>
<mi>a</mi>
<mo>+</mo>
<mn>4</mn>
<mo>=</mo>
<mn>28</mn>
<mo>+</mo>
<mn>4</mn>
<mspace linebreak="newline"></mspace>
<mo>=</mo>
<mn>32</mn>
</math>
Solution: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mi>a</mi>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>1</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>2</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>3</mn>
<mo>+</mo>
<mi>a</mi>
<mo>+</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>5</mn>
</mfrac>
<mspace linebreak="newline"></mspace>
<mn>30</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5</mn>
<mi>a</mi>
<mo>+</mo>
<mn>10</mn>
</mrow>
<mn>5</mn>
</mfrac>
<mspace linebreak="newline"></mspace>
<mn>30</mn>
<mo>×</mo>
<mn>5</mn>
<mo>=</mo>
<mn>5</mn>
<mi>a</mi>
<mo>+</mo>
<mn>10</mn>
<mspace linebreak="newline"></mspace>
<mn>5</mn>
<mi>a</mi>
<mo>=</mo>
<mn>150</mn>
<mo>−</mo>
<mn>10</mn>
<mspace linebreak="newline"></mspace>
<mn>5</mn>
<mi>a</mi>
<mo>=</mo>
<mn>140</mn>
<mspace linebreak="newline"></mspace>
<mi>a</mi>
<mo>=</mo>
<mn>28</mn>
<mspace linebreak="newline"></mspace>
<mo>∴</mo>
<mi>a</mi>
<mo>+</mo>
<mn>4</mn>
<mo>=</mo>
<mn>28</mn>
<mo>+</mo>
<mn>4</mn>
<mspace linebreak="newline"></mspace>
<mo>=</mo>
<mn>32</mn>
</math>
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