John volunteers at a shelter twice a month for 3 hours at a time. How many hours does he volunteer per year?

How many times does he volunteer in a year? ** He volunteers 2*12=

<<2*12=24>>24 times a year How many hours does he volunteer in a year? ** So he volunteers for 24*3=<<24*3=72>>72 hours #### 72 John puts $25 in his piggy bank every month for 2 years to save up for a vacation. He had to spend $400 from his piggy bank savings last week to repair his car. How many dollars are left in his piggy bank? How many months did John save money for? ** He saved money for 2 years, which is equal to 12 x 2 = <<12*2=24>>24 months. How much money did John save? ** The amount of money he saved is $25*24 = $<<25*24=600>>600. How many dollars are left in his piggy bank? ** But he spent some money so there is $600 - $400 = <<600-400=200>>200 left. #### 200 Five coaster vans are used to transport students for their field trip. Each van carries 28 students, 60 of which are boys. How many are girls? How many students are in the 5 vans? ** There are a total of 5 vans x 28 students = <<5*28=140>>140 students. How many students are girls? ** If 60 are boys, then 140 - 60 = <<140-60=80>>80 of these students are girls. #### 80 Bobby has 16 toy cars, and the number of cars he has increases by 50% every year. How many toy cars will Bobby have in three years? How many new cars will Bobby acquire in the first year? ** In the first year, Bobby will acquire 16 * .5 = <<16*.5=8>>8 new cars. How many cars will Bobby have after the first year? ** After the first year, he will have a total of 16 + 8 = <<16+8=24>>24 cars. How many new cars will Bobby acquire in the second year? ** In the second year, Bobby will acquire 24 * .5 = <<24*.5=12>>12 new cars. How many cars will Bobby have after the second year? ** After the second year, he will have 24 + 12 = <<24+12=36>>36 cars in total. How many new cars will Bobby acquire in the third year? ** In the third year, Bobby will acquire 36 * .5 = <<36*.5=18>>18 new cars. How many cars will Bobby have after the third year? ** After the third year, he will have 36 + 18 = <<36+18=54>>54 cars in total. #### 54 Last year Jessica paid $1000 for rent, $200 for food, and $100 for car insurance each month. This year her rent goes up by 30%, food costs increase by 50%, and the cost of her car insurance triples because she was at fault in an accident. How much more does Jessica pay for her expenses over the whole year compared to last year? How much does Jessica's rent go up? ** First find the increase in rent by multiplying last year's rent by 30%: $1000 * .3 = $<<1000*.3=300>>300 How much does Jessica's food cost increase? ** Then find the food cost increase by multiplying last year's costs by 50%: $200 * .5 = $<<200*.5=100>>100 How much does Jessica's car insurance cost increase? ** Then find the new car insurance price by multiplying last year's price by 3: $100 * 3 = $<<100*3=300>>300 How much more does Jessica pay for car insurance? ** Then subtract the cost of car insurance last year from this year's price to find the increase: $300 - $100 = $<<300-100=200>>200 How much more does Jessica pay for her expenses over the whole year compared to last year? ** Now find how much Jessica's monthly expenses increased by adding the increases in each of the three costs: $300 + $100 + $200 = $<<300+100+200=600>>600 How much more does Jessica pay for her expenses over the whole year compared to last year? ** Now multiply the increase per month by the number of months in a year to find the annual increase: $600/month * 12 months/year = $<<600*12=7200>>7200/year #### 7200 Randy just turned 12 and started playing the piano. His friend Sheila told him about the 10,000-hour rule which says, after 10,000 hours of practice, you become an expert or master in your field. If Randy wants to become a piano expert before he is 20, how many hours a day will he need to practice if he practices every day, Monday – Friday, and takes two weeks off for vacation each year? How many years until Randy is 20? ** Randy has 20 – 12 = <<20-12=8>>8 years until he is 20. How many hours a year will Randy need to practice? ** He must practice 10,000 hours / 8 years = <<10000/8=1250>>1,250 hours a year to become an expert. How many weeks of practice will Randy need? ** There are 52 weeks in a year – 2 weeks of vacation Randy plans to take = <<52-2=50>>50 weeks of practice for Randy. How many days of practice will Randy need each year? ** Randy will practice Monday – Friday, which is 5 days a week, so 50 weeks x 5 days = <<50*5=250>>250 days of practice each year. How many hours will Randy need to practice each day? ** Randy will need to practice 1250 hours / 250 days = <<1250/250=5>>5 hours each day. #### 5 Mike and Ted planted tomatoes. In the morning, Mike planted 50 tomato seeds while Ted planted twice as much as Mike. In the afternoon, Mike planted 60 tomato seeds while Ted planted 20 fewer tomato seeds than Mike. How many tomato seeds did they plant altogether? How many tomato seeds did Ted plant? ** Ted planted 2 x 50 = <<2*50=100>>100 tomato seeds. How many tomato seeds did Mike and Ted plant in the morning? ** So, Mike and Ted planted 50 + 100 = <<50+100=150>>150 tomato seeds in the morning. How many tomato seeds did Ted plant in the afternoon? ** In the afternoon, Ted planted 60 - 20 = <<60-20=40>>40 seeds. How many tomato seeds did Mike and Ted plant in the afternoon? ** Thus, Mike and Ted planted 60 + 40 = <<60+40=100>>100 tomato seeds in the afternoon. How many tomato seeds did Mike and Ted plant altogether? ** Therefore, they planted 150 + 100 = <<150+100=250>>250 tomato seed altogether. #### 250 In 6 months Bella and Bob will be celebrating their 4th anniversary. How many months ago did they celebrate their 2nd anniversary? How many months have they been together? ** First, we find their current point in time be realizing that 4 years is 4 sets of 12 months, meaning at that anniversary they will have been together 4*12=<<4*12=48>>48 months How many months ago did they celebrate their 2nd anniversary? ** Then, we subtract their 6 month difference, finding they are at 48-6=<<48-6=42>>42 months into their relationship. How many months were they together at their 2nd anniversary? ** Since 2 years would be 2*12=<<2*12=24>>24 months into the relationship. How many months ago did they celebrate their 2? ** We take the larger number, 42, and subtract the smaller number, 24 to find the difference in months, meaning it is 42-24= <<42-24=18>>18 months #### 18 A church has 120 members. 40% are adults. The rest are children. How many children more children are there than adults? How many adults are there? ** There are 48 adults because 120 x .4 = <<120*.4=48>>48 How many children are there? ** 60% of members are children because 100 - 40 = <<100-40=60>>60 How many children are there? ** There are 72 children because 120 x .6 = <<120*.6=72>>72 How many more children are there than adults? ** There are 24 more children than adults because 72 - 48 = <<72-48=24>>24 #### 24 Missy had a giant piggy bank in her bedroom. Every day she would search the house for change to put in her bank. After 4 years, the bank was opened and it contained $450 in change. If the second, third, and fourth-year she doubled the amount of money she put in the bank from the amount she had put in the previous year, how much money, in dollars, did she put in the bank the first year? Define a variable ** We let x be the amount of money she put in the bank the first year, How much money did Missy put in the bank the second year? ** Then the second year was 2*x, How much money did Missy put in the bank the third year? ** and the third year was 2*2*x=4*x, How much money did Missy put in the bank the fourth year? ** and the fourth year was 2*2*2*x=8*x. Write an equation ** And the total amount she put in the bank, $450, is the sum of all four years, or $450 = x+(2*x)+(4*x)+(8*x). Simplify ** This simplifies to $450=15*x. How much money did Missy put in the bank the first year? ** And therefore, the amount of money she put in the bank the first year was x=$<<30=30>>30. #### 30