A forester is planting trees. The forest already has 30 native trees. On Monday he triples the number of total trees in the forest by planting new trees. On Tuesday, he plants a third of the amount he planted on Monday. How many trees has the forester planted in total?

Define a variable ** Let M be the number of trees he plants on Monday.

How many trees were there on Monday? ** On Monday the forest was three times larger from the trees that were originally there and the M trees: 3*30 = 30 + M trees.

Write an equation ** So, 90=30+M.

How many trees did the forester plant on Monday? ** And, M =

<<60=60>>60 trees. How many trees did the forester plant on Tuesday? ** On Tuesday, he planted 60 trees / 3 = <<60/3=20>>20 trees. How many trees has the forester planted in total? ** In total, he has planted 60 trees + 20 trees = <<60+20=80>>80 trees. #### 80 Roy has 2 blue pens. He has twice as many black and 2 less than twice as many red than black pens. How many pens does Roy have in all? How many black pens does Roy have? ** Roy has 2 x 2 = <<2*2=4>>4 black pens. How many black pens does Roy have? ** Twice the number of black pens is 4 x 2 = <<4*2=8>>8. How many red pens does Roy have? ** So, there are 8 - 2 = <<8-2=6>>6 red pens. How many pens does Roy have in all? ** Therefore, Roy has 2 + 6 + 4 = <<2+6+4=12>>12 pens in all. #### 12 Devin teaches one math course per year. He taught Calculus for 4 years, Algebra for twice as many years, and Statistics for 5 times as long as he taught Algebra. How many years has Devin taught? How many years did Devin teach Calculus? ** Calculus: <<4=4>>4 years How many years did Devin teach Algebra? ** Algebra: 4(2)=8 years How many years did Devin teach Statistics? ** Statistics: 8(5)=<<8*5=40>>40 years How many years has Devin taught? ** Total number of years taught: 4+8+40=<<4+8+40=52>>52 years #### 52 Bonnie and Samuel went to the market together. Bonnie bought 8 apples. Samuel bought 20 more apples than Bonnie. Samuel then ate half of them and used 1/7 of them to make apple pie. How many apples does Samuel have left? How many apples did Samuel buy? ** Samuel bought 20+8 = <<20+8=28>>28 apples. How many apples did Samuel eat? ** Samuel ate 28/2 = <<28/2=14>>14 apples. How many apples did Samuel use to make apple pie? ** Samuel used 28/7 = <<28/7=4>>4 to make apple pie. How many apples does Samuel have left? ** Samuel has 28-14-4 = <<28-14-4=10>>10 apples left. #### 10 Carla, Kyle, and Tasha caught 36 fish. If Kyle and Tasha caught the same number of fish and Carla caught 8, how many fish did Kyle catch? How many fish did Kyle and Tasha catch? ** Kyle and Tasha caught 36 - 8 = <<36-8=28>>28 fish How many fish did Kyle catch? ** Kyle caught 28/2 = <<28/2=14>>14 fish #### 14 Randy got 90, 98, 92, and 94 in his first four quizzes. His goal is to get a 94 average on his 5 quizzes. What score should he get in the fifth quiz to reach his desired average? How many points are in the 5 quizzes? ** Since Randy wants to get an average of 94, then the sum of the 5 quizzes should be 94 x 5 = <<94*5=470>>470. How many points did Randy get in the first four quizzes? ** The sum of Randy's score for the first four quizzes is 90 + 98 + 92 + 94 = <<90+98+92+94=374>>374. How many points does Randy need to get in the fifth quiz? ** Thus, Randy needs to get 470 - 374 = <<470-374=96>>96 in his fifth quiz. #### 96 John has to pay taxes. He earned $100,000 for the year. He has $30,000 in deductions. The first $20,000 of taxable income is taxed at 10%. The rest is taxed at 20%. How much does he pay in taxes? How much is John's taxable income? ** His taxable income is 100,000-30,000=$<<100000-30000=70000>>70,000 How much does John pay in taxes at the lower rate? ** So he pays 20,000*.1=$<<20000*.1=2000>>2000 tax at the lower rate How much does John pay in taxes at the higher rate? ** He has to pay 70,000-20,000=$<<70000-20000=50000>>50,000 at the higher rate How much does John pay in taxes at the higher rate? ** The taxes for that is 50,000*.2=$<<50000*.2=10000>>10,000 How much does John pay in taxes? ** So his total tax bill is 10,000+2,000=$<<10000+2000=12000>>12,000 #### 12000 Frank has three less than half the number of cookies as Mike. Mike has three times as many cookies as Millie. If Millie has 4 cookies, how many cookies does Frank have? How many cookies does Mike have? ** Mike has 4 * 3 = <<4*3=12>>12 cookies. How many cookies does Frank have? ** Frank has 12 / 2 - 3 = <<12/2-3=3>>3 cookies #### 3 Marcus spends 20 minutes giving his dog a bath and half as long blow-drying her. Then he takes her for a walk along a 3-mile trail. If Marcus walks at 6 miles per hour, how much time does he spend with his dog total? How long does Marcus spend blow-drying his dog? ** First find the total amount of time Marcus spends blow-drying his dog: 20 minutes / 2 = <<20/2=10>>10 minutes How long does Marcus spend walking? ** Then find the time Marcus spends walking: 3 miles / 6 miles/hour = <<3/6=.5>>.5 hours How long does Marcus spend walking? ** Then convert that time to minutes: .5 hours * 60 minutes/hour = <<.5*60=30>>30 minutes How much time does Marcus spend total? ** Then add up the time Marcus spends washing, drying and walking to find the total time: 10 minutes + 20 minutes + 30 minutes = <<10+20+30=60>>60 minutes #### 60 Candice read 3 times as many books as Amanda in their school's Book Tournament. Kara read half the number of books that Amanda read, and Patricia read 7 times the number of books that Kara read. If Candice read 18 books, how many books did Patricia read? How many books did Amanda read? ** Amanda read 18/3 = <<18/3=6>>6 books. How many books did Kara read? ** Kara read 6/2 = <<6/2=3>>3 books. How many books did Patricia read? ** Patricia read 7 x 3 = <<7*3=21>>21 books. #### 21