44 Chapter 1 Real Numbers and Algebraic Expressions Translate each expression. Use x for the unknown quantity. 111. Half the sum of a number and 9 equals the difference between the number of 15. 112. Triple the difference of a number and 10 equals the sum of half the number and 5. 113. A number decreased by 3 is greater than 10 less than twice the number. 114. A number decreased by 12 is greater than half the sum of the number and 15. 115. Persia is 9 years older than Obie. If x represents Obie’s age, write an expression for Persia’s age. 116. Brent is 3 years younger than AJ. If x represents AJ’s age, write an expression for Brent’s age. 117. There was a 5% decrease in U.S./Canada movie admissions from 2009 to 2010. If x represents the number of movie admissions in 2009, write an expression for the number of movie admissions in 2010. (Source: http://www.mpaa.org) 118. The average price of a movie ticket in 2010 was $2.23 more than the average price of a movie ticket in 2001. If x represents the average price of a movie ticket in 2001, write an expression for the price of a movie ticket in 2010. (Source: http://www.mpaa.org) 119. Of the moviegoers in 2010, 23% of them are aged 25 to 39. If x represents the number of moviegoers, write an algebraic expression for the number of moviegoers who are aged 25 to 39. (Source: http://www.mpaa.org) 120. Referring to Exercise 119, write an algebraic expression for the number of moviegoers who are not aged 25 to 39. You Be the Teacher! Answer each student’s question or correct the student’s error, if any. 121. There was a 4.9% increase in the number of people who patronized a restaurant from 2010 to 2011. If x represents the number of people who patronized that restaurant in 2010, write an algebraic expression for the number of people who patronized the restaurant in 2011. Knox’s work: x + 0.49x 122. There was a 12% decrease in the number of memberships to a gym from 2009 to 2010. If x represents the number of people who had membership to the gym in 2009, write an expression for the number of people who had a gym membership in 2010. Vivienne’s work: 0.12x 123. Sandra: How do you fi nd the additive inverse when there are variables? 124. Dave: How do you fi nd the multiplicative inverse when there is a variable involved? GROUP ACTIVITY A Magical Mathematical Birthday Card For Part 1, begin with your birth month and follow Steps 1–12. For Part 2, use the variables as described to explain how the trick works. Part 1 1. Write the number of the month you were born, or enter it in your calculator. 2. Multiply this number by 4. 3. Add 13 to your result. 4. Multiply this number by 25. 5. Subtract 200 from your result. 6. Add the day of the month on which you were born to the previous result. 7. Multiply this number by 2. 8. Subtract 40 from your result. 9. Multiply this number by 50. 10. Add the last two digits of your birth year. 11. Subtract 10,500 from your result. 12. Put slashes in your final result, so that the digits are in groups of two, starting from the right. You should see your birth date displayed! Part 2 1. Let m = month, d = day, and y = last two digits of year you were born. 2. Write the algebraic statements that correspond to Steps 1–12. 3. Explain how this trick works.
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