Question 1203850
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Question: 
Members of a dancing club are asked which of four Latin dances they performed most recently. Their responses are summarized in the incomplete two-way relative frequency table below.
What percent of the members are ages 31 to 50 and most recently danced the samba?


Table Provided
<table border = "1" cellpadding = "5"><tr><td></td><td>Merengue</td><td>Bachata</td><td>Samba</td><td>Pasillo</td><td>Total</td></tr><tr><td>Ages 18 to 30</td><td>3%</td><td>18%</td><td>11%</td><td></td><td></td></tr><tr><td>Ages 31 to 50</td><td>7%</td><td>4%</td><td></td><td>1%</td><td></td></tr><tr><td>Ages 51 to 75</td><td></td><td>10%</td><td>5%</td><td>7%</td><td>34%</td></tr><tr><td>Total</td><td></td><td>32%</td><td></td><td>17%</td><td>100%</td></tr></table>


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I'll write A,B,C,D,E,F,G in the 7 blanks as shown below.
<table border = "1" cellpadding = "5"><tr><td></td><td>Merengue</td><td>Bachata</td><td>Samba</td><td>Pasillo</td><td>Total</td></tr><tr><td>Ages 18 to 30</td><td>3%</td><td>18%</td><td>11%</td><td>A</td><td>B</td></tr><tr><td>Ages 31 to 50</td><td>7%</td><td>4%</td><td>C</td><td>1%</td><td>D</td></tr><tr><td>Ages 51 to 75</td><td>E</td><td>10%</td><td>5%</td><td>7%</td><td>34%</td></tr><tr><td>Total</td><td>F</td><td>32%</td><td>G</td><td>17%</td><td>100%</td></tr></table>


It should be fairly clear that A or E is the best choice to start with.
I'll go with E.


Along the third row, the percentages must add to 34%
E+10+5+7 = 34
E+22 = 34
E = 34-22
E = 12
We'll replace E with 12%
<table border = "1" cellpadding = "5"><tr><td></td><td>Merengue</td><td>Bachata</td><td>Samba</td><td>Pasillo</td><td>Total</td></tr><tr><td>Ages 18 to 30</td><td>3%</td><td>18%</td><td>11%</td><td>A</td><td>B</td></tr><tr><td>Ages 31 to 50</td><td>7%</td><td>4%</td><td>C</td><td>1%</td><td>D</td></tr><tr><td>Ages 51 to 75</td><td>12%</td><td>10%</td><td>5%</td><td>7%</td><td>34%</td></tr><tr><td>Total</td><td>F</td><td>32%</td><td>G</td><td>17%</td><td>100%</td></tr></table>


Then add up the items in the first column
3+7+12 = 22
Therefore we replace F with 22%
<table border = "1" cellpadding = "5"><tr><td></td><td>Merengue</td><td>Bachata</td><td>Samba</td><td>Pasillo</td><td>Total</td></tr><tr><td>Ages 18 to 30</td><td>3%</td><td>18%</td><td>11%</td><td>A</td><td>B</td></tr><tr><td>Ages 31 to 50</td><td>7%</td><td>4%</td><td>C</td><td>1%</td><td>D</td></tr><tr><td>Ages 51 to 75</td><td>12%</td><td>10%</td><td>5%</td><td>7%</td><td>34%</td></tr><tr><td>Total</td><td>22%</td><td>32%</td><td>G</td><td>17%</td><td>100%</td></tr></table>


I'll let the student take over from here.
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