Antoinette weighs 7 less kilograms than twice Rupert's weight. Together they weigh 98 kilograms. How many kilograms does Antoinette weigh?

Define a variable ** Let R = Rupert's weight

How much does Antoinette weigh? ** Antoinette = 2R - 7

Write an equation ** R + 2R - 7 = 98

Simplify ** 3R = 105

How much does Rupert weigh? ** Rupert =

<<35=35>>35 kg How much does Antoinette weigh? ** Antoinette = 2 * 35 - 7 = <<2*35-7=63>>63 kg How many kilograms does Antoinette weigh? ** Antoinette weighs 63 kilograms. #### 63 Marcus has received a commission for as many paintings as possible. Marcus plans out his drawings so that his client can receive some of the paintings as soon as possible but it is still going to take a long time. On the first day, he paints 2 paintings. He then paints every day and each day, he paints twice as many paintings as he painted the day before. If he paints for 5 days, how many paintings will he have painted in total? How many paintings does Marcus paint on the second day? ** If Marcus creates 2 paintings on the first day, then he can paint 2 paintings * 2 = <<2*2=4>>4 paintings on the 2nd day. How many paintings does Marcus paint on the third day? ** So he paints 4 paintings * 2 = <<4*2=8>>8 paintings on the 3rd day. How many paintings does Marcus paint on the fourth day? ** He then paints 8 paintings * 2 = <<8*2=16>>16 paintings on the 4th day. How many paintings does Marcus paint on the fifth day? ** And finally paints 16 paintings * 2 = <<16*2=32>>32 paintings on the 5th day. How many paintings does Marcus paint in total? ** Marcus therefore has painted a total of 2 + 4 + 8 + 16 + 32 = <<2+4+8+16+32=62>>62 paintings. #### 62 Chris is trying to sell his car for $5200 and has gotten two price offers. One buyer offered to pay the full price if Chris would pay for the car maintenance inspection, which cost a tenth of Chris’s asking price. The other buyer agreed to pay the price if Chris replaced the headlights for $80 and the tires for three times as much. What is the difference between the amounts Chris will earn from the two offers? How much would Chris earn from the first buyer? ** Chris would earn 5200 - 5200 / 10 = 5200 - 520 = $<<5200-5200/10=4680>>4680 from the first buyer. How much would Chris earn from the second buyer? ** He would earn 5200 - 80 - 80 * 3 = 5200 - 80 * 4 = 5200 - 320 = $<<5200-80-80*3=4880>>4880 from the second buyer. What is the difference between the amounts Chris will earn from the two offers? ** The difference between Chris’s earnings would be 4880 - 4680 = $<<4880-4680=200>>200. #### 200 Sam invested $10,000 and earned 20% interest compounded for 3 years. He then invested more until he had three times as much invested. The next year, he got a 15% return on his investment. How much money does he have now? How much money did Sam have after one year? ** After one year, Sam had $10,000 * 1.2 = $<<10000*1.2=12000>>12,000. How much money did Sam have after two years? ** After two years, he had $12,000 * 1.2 = $<<12000*1.2=14400>>14,400. How much money did Sam have after the third year? ** After the third year, he had $14,400 * 1.2 = $<<14400*1.2=17280>>17,280. How much money did Sam have after investing more? ** He then invested more money until he had 3 * $17,280 = $<<3*17280=51840>>51,840. How much money did Sam have after the first year? ** The first year after that, he had $51,840 * 1.15 = $<<51840*1.15=59616>>59,616. #### 59,616 Avery opens a flower shop. She ties 8 bunches of flowers with 9 flowers in each bunch. How many bunches would she have if she put 12 flowers in each bunch instead? How many flowers does Avery have? ** She has a total of 8 * 9 = <<8*9=72>>72 flowers. How many bunches would she have if she put 12 flowers in each bunch instead? ** Dividing them in bunches of 12 will give her 72 / 12 = <<72/12=6>>6 bunches of flowers. #### 6 Janet has a business selling custom collars for dogs and cats. If it takes 18 inches of nylon to make a dog collar and 10 inches to make a cat collar, how much nylon does she need to make 9 dog collars and 3 cat collars? How many inches of nylon are used for the dog collars? ** First find the total number of inches of nylon used for the dog collars: 18 inches/dog collar * 9 dog collars = 162 inches How many inches of nylon are used for the cat collars? ** Then find the total number of inches of nylon used for the cat collars: 10 inches/cat collar * 3 cat collars = 30 inches How many inches of nylon does Janet need to make 9 dog collars and 3 cat collars? ** Then add the nylon needed for the cat and dog collars to find the total amount needed: 162 inches + 30 inches = <<162+30=192>>192 inches #### 192 Ken can do 20 sit-ups without stopping. Nathan can do twice as many, and Bob can do half the number of Ken and Nathan's combined sit-ups. How many more sit-ups can Bob do compared to Ken? How many sit ups can Nathan do? ** Nathan can do 20 x 2 = <<20*2=40>>40 sit ups. How many sit-ups can Ken and Nathan do together? ** Ken and Nathan's combined number is 20 + 40 = <<20+40=60>>60 sit-ups. How many sit-ups can Bob do? ** Bob can do 60/2 = <<60/2=30>>30 sit-ups. How many more sit-ups can Bob do compared to Ken? ** Bob can do 30 - 20 = <<30-20=10>>10 more sit-ups than Ken. #### 10 Ben will receive a bonus of $1496. He chooses to allocate this amount as follows: 1/22 for the kitchen, 1/4 for holidays and 1/8 for Christmas gifts for his 3 children. How much money will he still have left after these expenses? How much money will Ben spend on the kitchen? ** Ben's spending for the kitchen is $1496 x 1/22 = $<<1496*1/22=68>>68. How much money will Ben spend on holidays? ** Ben's spending for holidays is $1496 x 1/4 = $<<1496*1/4=374>>374. How much money will Ben spend on Christmas gifts? ** Ben's spending for children's gifts is $1496 x 1/8 = $<<1496*1/8=187>>187. How much money will Ben spend in total? ** The total amount spent is $68 + $374 + $187 = $<<68+374+187=629>>629. How much money will Ben still have left after these expenses? ** So, Ben still has $1496 - $629 = $<<1496-629=867>>867 left. #### 867 Nina wants to give presents to her children. She buys three toys at $10 each, two packs of basketball cards at $5 each, and five shirts at $6 each. How much does she spend in all? How much do the toys cost? ** Three toys cost 3 x $10 = $<<3*10=30>>30. How much do the cards cost? ** Two packs of basketball cards cost 2 x $5 = $<<2*5=10>>10. How much do the shirts cost? ** And, five shirts cost 5 x $6 = $<<5*6=30>>30. How much does Nina spend in all? ** Therefore, Nina spends a total of $30 + $10 + $30 = $<<30+10+30=70>>70 in all. #### 70 A woman is trying to decide whether it will be quicker to take an airplane or drive herself to a job interview. If she drives herself, the trip will take her 3 hours and 15 minutes. If she takes an airplane, she will first need to drive 10 minutes to the airport, and then wait 20 minutes to board the plane. After that, she will be on the airplane for one-third of the time it would have taken her to drive herself before landing in the destination city. Finally, it will take her an additional 10 minutes to get off the airplane and arrive at her interview site after the plane lands. Given this information, how many minutes faster is it for her to take the airplane? How many minutes does it take to drive? ** First, we must convert the driving time of 3 hours and 15 minutes to minutes. Since there are 60 minutes in an hour, driving takes a total of 3*60 + 15 = <<3*60+15=195>>195 minutes. How many minutes will the woman be on the airplane? ** Next, the woman will be on the airplane for one-third of 195 minutes, or 195/3 = <<195/3=65>>65 minutes. How many minutes will the airplane trip take? ** Therefore, in total, the airplane trip will take the woman 10 + 20 + 65 + 10 = <<10+20+65+10=105>>105 minutes. How many minutes faster is it for her to take the airplane? ** Thus, the airplane trip is 195 - 105 = <<195-105=90>>90 minutes faster than driving herself to the interview. #### 90