Erin is sorting through the library books to decide which ones to replace. She finds 8 less than 6 times as many obsolete books as damaged books. If she removes 69 books total, how many books were damaged?

Let o be the number of obsolete books and d be the number of damaged books. We know that o + d = 69 and o = 6d - 8.

Substituting the first equation into the second equation, we get 6d - 8 + d = 69

Combining like terms, we get 7d - 8 = 69

Adding 8 to both sides, we get 7d = 77

Dividing both sides by 7, we get d = 11

#### 11

Tyrone empties his piggy bank and finds two $1 bills, a $5 bill, 13 quarters, 20 dimes, 8 nickels, and 35 pennies. How much money does Tyrone have?

He has $2 in $1 bills because 2 times 1 equals

<<2*1=2>>2. He has $5 in $5 bills because 1 times 5 equals <<5*1=5>>5. He has $3.25 in quarters because 13 times .25 equals <<13*.25=3.25>>3.25 He has $2 in dimes because 20 times .1 equals <<20*.1=2>>2. He has $.40 in nickels because 8 times .05 equals .4. He has $.35 in pennies because 35 times .01 equals .35. He has $13 because 2 plus 5 plus 3.25 plus 2 plus .4 plus .35 equals <<2+5+3.25+2+.4+.35=13>>13. #### 13 James sells a $500,000 house for 20% over market value. He splits the revenue with his 3 brothers. How much does each person get after taxes take away 10%? He sells the house for 1+.2=<<1+.2=1.2>>1.2 times its value So he sells the house for 500,000*1.2=<<500000*1.2=600000>>600,000 He splits the money 1+3=<<1+3=4>>4 ways So each person gets 600,000/4=$<<600000/4=150000>>150,000 before taxes Taxes take away 150,000*.1=$<<150000*.1=15000>>15,000 So each person gets 150,000-15,000=$<<150000-15000=135000>>135,000 #### 135000 Austin and Jake start descending from the 9th floor of a building at the same time. Austin uses the elevator and Jake uses the stairs, descending 3 steps every second. The stairs have 30 steps across each floor. If the elevator will take a minute to get to ground level, how many seconds later will Jake get to the ground floor? Jake has to descend 30 steps on 9 floors for a total of 9*30 = <<30*9=270>>270 steps He descends 3 steps every second so he will descend 270 steps in 270/3 = <<270/3=90>>90 seconds. Austin will get down after only a minute (60 seconds) so Jake will get down 90-60 = <<90-60=30>>30 seconds later. #### 30 Diane is playing poker with her friends and is not having very good luck. She starts with $100 and wins 5 hands for a total of $65 dollars to add to her $100. Emboldened, she begins betting bigger and riskier and ends up losing all her money and owing her friends $50. How much money did Diane lose in all? Diane started with $100 and won $65, for a total mid-game of $<<100+65=165>>165. However, she ended up owing her friends $50, so she lost $165 + $50 = $<<165+50=215>>215 she lost in all. #### 215 Bernie has a collection of 18 unique postcards. He decided to sell half his collection for $15 per postcard. After he has successfully sold his postcards he decided to spend all the earned money to buy new postcards for $5 each. How many postcards does Bernie have after all his transactions? Half of Bernie's collection means 18 * 0.5 = <<18*0.5=9>>9 postcards. So he was able to sell 9 postcards for 9 * 15 = $<<9*15=135>>135. He decided to spend all of his money on new postcards for $5 each, so he was able to buy 135 / 5 = 27 new postcards. This means Bernie has 9 + 27 = <<9+27=36>>36 postcards after all. #### 36 Heath spent his weekend helping at his uncle’s farm planting carrots. He planted 400 rows of carrots with 300 plants in each row. He used a machine to get the planting done and it took him 20 hours. How many carrots did he plant each hour? Heath planted 400 rows x 300 plants = <<400*300=120000>>120,000 carrot plants. He planted 120,000 plants in 20 hours, or 120,000 / 20 = <<120000/20=6000>>6,000 plants per hour. #### 6,000 Jackie loves to climb trees. She climbed a 1000 foot tall tree. Then she climbed 2 trees that were half as tall as the first tree. She finished by climbing a tree that was 200 feet taller than her first tree. What was the average height of the trees that Jackie climbed? Jackie climbed 2 trees that were 1/2 * 1000 feet = 500 feet tall each. Jackie climbed a final tree that was 1000 + 200 feet = <<1000+200=1200>>1200 feet. In total, the 4 trees Jackie climbed were 1000 feet + 500 feet + 500 feet + 1200 feet = <<1000+500+500+1200=3200>>3200 feet. The average height tree that Jackie climbed was 3200 feet / 4 trees = <<3200/4=800>>800 feet tall. #### 800 Every 2 years, the number of swans at Rita's pond doubles. Currently, there are 15 swans in the pond. How many swans will there be in ten years? If currently there are 15 swans in the pond, in two years' time there will be 15*2=<<15*2=30>>30 swans. In another two years, the number of swans in the pond will double to 2*30=<<2*30=60>>60 swans In another two years, the number of swans in the pond will double to 2*60=<<2*60=120>>120 swans If after 6 years there are 120 swans in the pond, in eight years times there will be 2*120=240 swans In another two years, which is 10 years, there will be 2*240=<<2*240=480>>480 swans in the pond #### 480 John has just turned 39. 3 years ago, he was twice as old as James will be in 6 years. If James' older brother is 4 years older than James, how old is James' older brother? John was 39-3=<<39-3=36>>36 years old 3 years ago So that means in 6 years James will be 36/2=<<36/2=18>>18 years old So right now James is 18-6=<<18-6=12>>12 years old So James's older brother is 12+4=<<12+4=16>>16 years old #### 16