Jean has three times as much money as Jane. They have a combined total of $76. How much money does Jean have?

Define a variable ** Let's assume the total amount of money that Jane has is m.

How much money does Jean have? ** Since Jean has 3 times as much money as Jane, he has 3*m=3m

How much money does Jean and Jane have combined? ** Combined, Jean and Jane have a total of m+3m = $76

How much money does Jean and Jane have combined? ** This evaluates to 4m=$76

How much money does Jane have? ** The total amount of money that Jane has, represented by m, is m=$76/4

How much money does Jane have? ** Jane has m=$

<<19=19>>19 How much money does Jean have? ** Since Jean has three times as much money as Jane, Jean has 3*$19=$57 #### 57 Carter grew 9 plants with 3 seed packets. How many more seed packets does Carter need to have a total of 12 plants in his backyard? How many plants does Carter grow with 1 seed packet? ** If he grows 9 plants with 3 seed packets, he grows 9/3=<<9/3=3>>3 plants with 1 seed packet. How many more seed packets does Carter need to have a total of 12 plants in his backyard? ** Since 1 seed packet grows 3 plants, he'll need 1 more to make the plants 12. #### 1 Kimberly went hiking and took a 4-liter bottle full of water with her. The first time she drank from it, she consumed a quarter of the water in the bottle. Later on, she drank 2/3rd of the remaining water. How much water is left in the bottle (in liters)? How much water did Kimberly drink the first time? ** Her first drink consumed 1/4 * 4 = <<1/4*4=1>>1 liter of water. How many liters of water were left after the first drink? ** Thus there were 4 - 1 = <<4-1=3>>3 liters of water left in the bottle. How much water did Kimberly drink the second time? ** Next, she drank 2/3 * 3 = <<2/3*3=2>>2 liters. How many liters of water were left after the second drink? ** Thus, there were 3 - 2 = <<3-2=1>>1 liters remaining. #### 1 Micah drank 1.5 liters of water in the morning. Then she drank three times that much water in the afternoon. How many liters of water did she drink from the morning until the afternoon? How many liters did Micah drink in the afternoon? ** Micah drank 1.5 x 3 = <<1.5*3=4.5>>4.5 liters in the afternoon. How many liters of water did Micah drink in total? ** She drank a total of 1.5 + 4.5 = <<1.5+4.5=6>>6 liters of water. #### 6 Mr. and Mrs. Hugo went on a road trip. On the first day, they traveled 200 miles. On the second day, they traveled 3/4 as far. On the third day, they traveled 1/2 as many miles as the first two days combined. How many miles did they travel for 3 days? How many miles did they travel on the second day? ** On the second day, Mr. and Mrs. Hugo traveled 200 x 3/4 = <<200*3/4=150>>150 miles. How many miles did they travel in the first two days? ** They traveled a total of 200 + 150 = <<200+150=350>>350 miles in the first two days. How many miles did they travel on the third day? ** On the third day, they traveled 350 x 1/2 = <<350*1/2=175>>175 miles. How many miles did they travel for 3 days? ** So, Mr. and Mrs. Hugo traveled a total of 200 + 150 + 175 = <<200+150+175=525>>525 miles for 3 days. #### 525 Paul earns $12.50 for each hour that he works. He then has to pay 20% for taxes and fees. After working 40 hours, Paul receives his paycheck. If he spends 15% of his paycheck on gummy bears, how much, in dollars, does he have left? How much does Paul earn in total? ** His pay before taxes and fees is $12.50 x 40 hours = $<<12.5*40=500>>500. How much does Paul pay in total? ** He pays $500 * 0.20 = $<<500*0.20=100>>100 for taxes and fees. How much money does Paul have left? ** Then he had $500 - $100 = $<<500-100=400>>400 remaining money. How much does Paul spend on gummy bears? ** He takes out $400 * 0.15 = $<<400*0.15=60>>60 for his gummy bears. How much money does Paul have left? ** So he's left with $400 - $60 = $<<400-60=340>>340. #### 340 John is a door-to-door salesman. He visits 50 houses a day. 20% of them buy something from them. Of those that buy something half buy a $50 set of knives and the other half buy a $150 set of knives. How much does he sell a week when he works 5 days a week? How many houses buy from him per day? ** There are 50*.2=<<50*.2=10>>10 houses buying from him per day How many houses buy each type of knife set? ** Of those 10/2=<<10/2=5>>5 buy each type of knife set How much does he get from the cheap set? ** So he gets 5*50=$<<5*50=250>>250 per day from the cheap set How much does he get from the expensive set? ** He also gets 5*150=$<<5*150=750>>750 from the expensive set How much does he make in total? ** So he makes a total of 250+750=$<<250+750=1000>>1000 per day How much does he make in a week? ** That means he makes 1000*5=$<<1000*5=5000>>5000 #### 5000 Joseph wants to go to Boston for a road trip. If he takes route A, it will take him 5 hours to arrive; but if he takes route B, it will only take him 2 hours to arrive at his destination. How much time will he save if he takes route B to Boston and back to his home? How many hours will he spend if he takes route A? ** He will spend 5 x 2 = <<5*2=10>>10 hours if he takes route A. How many hours will he spend if he takes route B? ** Meanwhile, he will spend 2 x 2 = <<2*2=4>>4 hours if he takes route B. How much time will he save if he takes route B? ** Therefore, Joseph can save 10 - 4 = <<10-4=6>>6 hours if he takes route B both ways. #### 6 Elias uses a bar of soap every month. If each bar of soap costs $4, how much does he spend on bars of soap in two years? How much does Elias spend on bars of soap in a year? ** A year is 12 months, so Elias spends 4 * 12 = $<<4*12=48>>48 per year on bars of soap. How much does Elias spend on bars of soap in two years? ** In two years, he spends 2 * 48 = $<<2*48=96>>96 on bars of soap. #### 96 It’s exam season and Tristan has several exams to prepare for. On Monday, he studies for 4 hours then studies for twice this long on Tuesday. On Wednesday, Thursday, and Friday he studies for 3 hours each day. He wants to study for a total of 25 hours over the week and divides the remaining amount of study time evenly between Saturday and Sunday. How many hours does Tristan spend studying on Saturday? How many hours does Tristan study on Tuesday? ** On Tuesday, Tristan studies twice as long as he did on Monday and this amounts to 4 hours * 2 = <<4*2=8>>8 hours. How many hours does Tristan study in the first 5 days of the week? ** So in the first 5 days of the week, he studies for a total of 4 hours Monday + 8 hours Tuesday + 3 hours Wednesday + 3 hours Thursday + 3 hours Friday = 21 hours. How many hours does Tristan have left to study? ** He therefore has 25 planned hours – 21 used hours = <<25-21=4>>4 hours left to study. How many hours does Tristan spend studying on Saturday? ** As he splits his time evenly over 2 days, he spends 4 hours / 2 = <<4/2=2>>2 hours studying on Saturday. #### 2