document.write( "Question 1151468: A 40-year-old man has three daughters, ages 6, 3 and 1. In how many years will the combined ages of his daughters equal 80% of his age? \n" ); document.write( "
Algebra.Com's Answer #773220 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "The question asks \"In how many years will the combined ages of his daughters equal 80% of his age?\". Since we don't know right now, let's just call that x.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = number of years that go by\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Currently his daughters, who we'll call A, B, C for shorthand, are ages 6, 3 and 1. \n" ); document.write( "A = 6 \n" ); document.write( "B = 3 \n" ); document.write( "C = 1 \n" ); document.write( "Those are the current ages or present day ages.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If we add on x years, then \n" ); document.write( "A' = 6+x \n" ); document.write( "B' = 3+x \n" ); document.write( "C' = 1+x \n" ); document.write( "represent the future ages of each daughter\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Their combined ages in that time would be \n" ); document.write( "A' + B' + C' = (6+x)+(3+x)+(1+x) \n" ); document.write( "A' + B' + C' = 3x+10\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "----------------------\r \n" ); document.write( "\n" ); document.write( "The father is currently 40 years old. After x years go by, he is going to be 40+x years old. \n" ); document.write( "80% of this is (80/100)*(40+x) = 0.80*(40+x) = 32+0.8x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Set 32+0.8x and 3x+10 equal to each other, then solve for x \n" ); document.write( "3x+10 = 32+0.8x \n" ); document.write( "3x-0.8x = 32-10 \n" ); document.write( "2.2x = 22 \n" ); document.write( "x = 22/2.2 \n" ); document.write( "x = 10\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "---------------------- \n" ); document.write( "If x = 10 years go by, then the daughters' ages will update to \n" ); document.write( "A' = 6+x = 6+10 = 16 \n" ); document.write( "B' = 3+x = 3+10 = 13 \n" ); document.write( "C' = 1+x = 1+10 = 11 \n" ); document.write( "Giving a combined sum of A'+B'+C' = 16+13+11 = 40 \n" ); document.write( "Let p = 40.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "At the same time, the father goes from age 40 to age 50 after 10 years. \n" ); document.write( "Let q = 50.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note how p/q = 40/50 = 0.80 = 80% \n" ); document.write( "Showing that the combined ages, 10 years into the future, of the daughters represents 80% of the father's future age during the same timespan. \r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answer: 10 years \n" ); document.write( " \n" ); document.write( " |