Section 1.3 Properties of Real Numbers and Simplifying Algebraic Expressions 39 5b. According to the U.S. Census Bureau statistics, people with a bachelor’s degree earn nearly twice as much as those with only a high school diploma. If x represents the earnings of a high school graduate, write an expression that represents the earnings of a person with a bachelor’s degree. Solution 5b. Let x represent the earnings of a high school graduate. The earnings of a college graduate are twice as much as the earnings of a high school graduate, or 2x. 5c. According to www.collegeboard.com, the average published tuition and fee charges for in-state students at four-year public colleges in 2010–2011 is $555 more than the average published tuition and fee charges in 2009–2010. If x represents the average tuition and fee charges in 2009–2010, write an expression that represents the average tuition and fee charges in 2010–2011. Solution 5c. Let x represent the average tuition and fees for 2009–2010. The average fees for 2010–2011 are $555 more than the average fees for 2009–2010, so the expression for the average tuition and fees for 2010–2011 is x + 555 5d. In August 2011, the national median home price fell approximately 5.1% from the national median home price in 2010. The 2010 median home price was about $177,344. Write an equation that represents this situation if x is the national median home price in August 2011. (Source: http://www.realestateabc.com/ outlook.htm) Solution 5d. Let x represent the national median home price in August 2011. The median home price in August 2011 is equal to the median home price in 2010 minus the amount of decrease. The decrease amount is 5.1% of the price in 2010. So, the equation is Price in 2010 - decrease amount is the median price in August 2011. x - 0.051x = 177,344 5e. Shawn has a collection of dimes and quarters. He has seven fewer dimes than quarters. i. If x represents the number of quarters, write an expression for the number of dimes he has collected. ii. Write expressions for the value of the quarters and the value of the dimes in dollars. iii. If Shawn’s collection is worth $6.30, write an equation that represents the total value of the collection. Solution 5e. i. Let x represent the number of quarters. Since there are seven fewer dimes than quarters, the number of dimes can be represented by x - 7. ii. The value of one quarter is $0.25, the value of two is 0.25(2) = $0.50. So, the value of x quarters is 0.25x. The value of one dime is $0.10, the value of two is 0.10(2) = 0.20. So, the value of x - 7 dimes is 0.10(x - 7). iii. The value of the collection is the value of the quarters plus the value of the dimes. So, an equation that represents the total value is 0.25x + 0.10(x - 7) = 6.30
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above