Yuan is 7 years older than his brother David and twice his age. How old is David?

How old is Yuan? ** Let x be David's age. Yuan is seven years older than David, 7 + x = Y years.

How old is Yuan? ** Yuan is also twice David's age, 2 * x = Y years.

How old is Yuan? ** Since these two equations equal the same thing, we can write: 7 + x = 2 * x.

How old is David? ** Subtracting x from both sides we get 7 = x, so David is 7 years old.

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Carla is taking attendance for her sixth-grade class. She knows that 2 students are in the restroom, and one less than three times that number of students are absent. If there are four rows with six desks each that are all 2/3 full, how many students does Carla teach, including the ones in and out of the classroom?

How many students are absent? ** First find the number of absent students: 2 students * 3 - 1=

<<2*3-1=5>>5 students How many students are in each row? ** Now find the number of students in each row of desks: 6 desks/row * 2 students / 3 desks = 4 students/row How many students are in all the rows? ** Now find the number of students in all the rows: 4 rows * 4 students/row = <<4*4=16>>16 students How many students does Carla teach? ** Now add the students that are absent or in the bathroom: 16 students + 2 students + 5 students = <<16+2+5=23>>23 students #### 23 If Clover goes for a 1.5-mile walk in the morning and another 1.5-mile walk in the evening, every day, how many miles does he walk in 30 days? How many miles does Clover walk in the morning? ** He walks 1.5 miles in the morning and 1.5 miles in the evening so that’s 1.5+1.5 = <<1.5+1.5=3>>3 miles How many miles does Clover walk in 30 days? ** If he walks 3 miles everyday, for 30 days then he walks 3*30 = <<3*30=90>>90 miles in 30 days #### 90 Tyler has 21 CDs. He gives away a third of his CDs to his friend. Then he goes to the music store and buys 8 brand new CDs. How many CDs does Tyler have now? How many CDs does Tyler give away? ** Tyler gives away 21 / 3 = <<21/3=7>>7 CDs How many CDs does Tyler have after giving away a third of his CDs? ** After giving away a third of his CDs, Tyler has 21 - 7 = <<21-7=14>>14 CDs How many CDs does Tyler have after buying new CDs? ** After buying new CDs, Tyler has 14 + 8 = <<14+8=22>>22 CDs #### 22 Steve owns a lake shop that sells fish. He has a stock of 200 fish. He sells 50 fish and because his refrigerators stop working a third of the remaining fish become spoiled. A new stock of 200 more fish arrives. How many fish does he have in stock now? How many fish does he have left? ** If he had 200 fish and sells 50, he is left with 200 - 50 = <<200-50=150>>150 fish How many fish become spoiled? ** If a third of them get spoiled 1/3 * 150 = <<150*1/3=50>>50 fish get spoiled How many fish does he have left? ** The remaining number of fish is now 150 - 50 = <<150-50=100>>100 How many fish does he have in stock now? ** He then gets 200 more to make 100 + 200 = <<100+200=300>>300 fish #### 300 Tabitha and her friends were excited to go to the Christmas parade because they knew candy would be thrown to the crowd from the floats. Tabitha caught 22 pieces of candy. Stan caught 13 pieces. Julie caught half the amount of candy as Tabitha caught and Carlos caught twice as much candy as Stan. How many pieces in total did the friends catch? How many pieces of candy did Julie catch? ** Julie caught half the amount of Tabitha's 22 pieces so 22/2 = <<22/2=11>>11 pieces of candy caught by Julie How many pieces of candy did Carlos catch? ** Carlos caught twice the amount of candy as Stan's 13 pieces so 2 * 13 = <<2*13=26>>26 pieces of candy caught by Carlos How many pieces of candy did Tabitha, Stan, Julie and Carlos catch? ** All together, Tabitha caught 22 pieces, Stan had 13, Julie had 11 and Carlos had 26, so there were a total of 22+13+11+26 = <<22+13+11+26=72>>72 pieces of candy #### 72 Tom cannot afford a normal doctor, so he goes to a discount clinic that is 70% cheaper. It takes two visits, though, instead of 1. A normal doctor charges $200 for a visit. How much money does he save? How much was each visit cheaper? ** Each of Tom's visits was 200*.7=$<<200*.7=140>>140 cheaper How much did Tom pay for each visit? ** So he paid $200 - $140 = $<<200-140=60>>60 per visit How much did Tom pay in total? ** That means he paid $60 * 2 = $<<60*2=120>>120 How much money did Tom save? ** So he saved $200 - $120 = $<<200-120=80>>80 #### 80 Every Sunday, Sean picks up 1 almond croissant and 1 salami and cheese croissant that are $4.50 each. He also grabs a plain croissant for $3.00 and a loaf of focaccia for $4.00. On his way home he stops and picks up 2 lattes for $2.50 each. How much did he spend? How much are the almond and salami and cheese croissants? ** The almond croissant and the salami and cheese croissant are $4.50 each so that's 2*4.50 = $9.00 How much are the lattes? ** He buys 2 lattes that are $2.50 each so that's 2*2.50 = $<<2*2.50=5.00>>5.00 How much did Sean spend? ** The flavored croissants are $9.00, the lattes are $5.00 and he also grabbed a plain croissant for $3.00 and focaccia for $4.00 for a total of 9+5+3+4 = $<<9+5+3+4=21.00>>21.00 #### 21 Bingley has 5 bracelets. Kelly gives Bingley a fourth of her 16 bracelets. Then Bingley gives a third of his bracelets to his little sister. How many bracelets does Bingley have remaining? How many bracelets does Kelly give to Bingley? ** Kelly gives Bingley 16 / 4 = <<16/4=4>>4 bracelets How many bracelets does Bingley have? ** Bingley has 5 + 4 = <<5+4=9>>9 bracelets How many bracelets does Bingley give to his little sister? ** Bingley gives his little sister 9 / 3 = <<9/3=3>>3 bracelets How many bracelets does Bingley have remaining? ** In the end, Bingley has 9 - 3 = <<9-3=6>>6 bracelets remaining #### 6 Matt needs to buy new plates for his home. He only wants to do dishes once a week. Three days a week it is only him and his son eating and they use 1 plate each. On the remainder of the days, his parents join them and everyone uses 2 plates that day. How many plates does he need to buy? How many people are eating on the 3 days? ** So for 3 of the days, there are 1+1=2 people eating How many plates do they use on those days? ** So for those days they use 3*2=<<3*2=6>>6 plates How many days do the parents join them? ** On 7-3=4 days the parents join them How many people are eating on those days? ** On those days there are 2+2=<<2+2=4>>4 people eating How many plates do they use on those days? ** They use 4*2=<<4*2=8>>8 plates How many plates do they use in total? ** So they use 8*4=<<8*4=32>>32 plates How many plates do they use in total? ** That means they use a total of 32+6=<<32+6=38>>38 plates #### 38