Ten friends decide to get an end-of-year gift for their teacher. They plan to split the cost of the gift equally. But four of the group drop out. The remaining friends split the cost equally among themselves. If each share is now $8 more, how much does the gift cost, in dollars?

Define a variable ** Let N be the original price each friend was going to pay.

Write an equation ** 10N=6(N+8)

Simplify ** 10N=6N+48

Subtract 4N ** 4N=48

Divide by 4 ** N=

<<12=12>>12 How much does the present cost? ** Then the present costs 10*12=<<10*12=120>>120. #### 120 The girl scouts earned $30 total from selling delicious cookies. They want to go to the pool. It will cost them $2.50 per person to go and 10 people are going. What is the amount left? How much did the girls pay? ** The girls paid $2.50/person * 10 people = $<<2.5*10=25>>25. How much money do the girls have left? ** The girls have $30 - $25 = $<<30-25=5>>5 left. #### 5 Sam works at the Widget Factory, assembling Widgets. He can assemble 1 widget every 10 minutes. Jack from the loading dock can help assemble widgets when he doesn't have anything else to do. When he helps, they put together 2 complete widgets every 15 minutes. Recently the factory hired Tony to help assemble widgets. Being new to the job, he doesn't work as fast as Sam or Jack. Yesterday Sam worked for 6 hours before he had to leave work early for a dentist appointment. Jack was able to help out for 4 hours before he had to go back to the loading dock to unload a new shipment of widget materials. Tony worked the entire 8-hour shift. At the end of the day, they had completed 68 widgets. How long does it take Tony to assemble a Widget, in minutes? How many widgets does Sam complete in 10 minutes? ** Sam completes a widget every 10 minutes. How many minutes does Jack take to complete a widget? ** When Jack helps they finish 2 in 15 minutes. Sam has finished 1 widget and has begun working on another one, and Jack finishes the second one at 15 minutes. So it takes Jack 15 minutes to complete a widget. How many widgets did Sam complete yesterday? ** Sam worked for 6 hours yesterday, so he was able to complete 6 hours * 60 minutes per hour / 10 minutes per widget = <<6*60/10=36>>36 widgets. How many widgets did Jack complete yesterday? ** Jack worked for 4 hours, so he was able to complete 4 hours * 60 minutes per hour / 15 minutes per widget = <<4*60/15=16>>16 widgets. How many widgets did Tony personally complete? ** Sam, Jack, and Tony were able to complete 68 widgets together. So of those, Tony personally completed 68 widgets - 36 widgets - 16 widgets = <<68-36-16=16>>16 widgets. How many minutes does it take Tony to complete a widget? ** It took Tony 8 hours to complete those 16 widgets, so he takes 8 hours * 60 minutes per hour / 16 widgets = <<8*60/16=30>>30 minutes per widget. #### 30 Karen is packing her backpack for a long-distance hike. She packs 20 pounds of water, 10 pounds of food, and 20 pounds of gear. During her hike, she drinks 2 pounds of water per hour and eats 1/3rd the weight of food per hour as water per hour. How much weight is she carrying after six hours? How much food does Karen eat every hour? ** First find the weight of food Karen eats every hour: 2 pounds * 1/3 = 2/3 pounds food. How much weight does Karen's backpack lose every hour? ** Then find the total amount of weight Karen's backpack loses per hour she hikes: 2 pounds water/hour + 2/3 pound food/hour = 8/3 pounds/hour. How much weight does Karen lose in 6 hours? ** Multiply this by the number of hours she hikes to find the total amount of weight she loses: 8/3 pounds/hour * 6 hours = <<8/3*6=16>>16 pounds. How much weight does Karen start with? ** Add the weight of all her items to find total starting weight: 20 pounds + 10 pounds + 20 pounds = <<20+10+20=50>>50 pounds. How much weight does Karen have after 6 hours? ** Then subtract the weight she loses from the starting weight to find the weight after 6 hours: 50 pounds - 16 pounds = <<50-16=34>>34 pounds #### 34 Kimberley, Ela, and Houston all are sent to collect firewood by their grammy. Kimberley collects ten pounds of firewood, and Houston collects 12 pounds of firewood. If the three of them managed to collect a total of 35 pounds of firewood, how many pounds were collected by Ela? How many pounds of firewood did Kimberley and Houston collect? ** Kimberley and Houston collected 10+12 = <<10+12=22>>22 pounds of firewood. How many pounds of firewood did Ela collect? ** You can find how much Ela collected by subtracting that amount from the total amount collected: 35-22 = <<35-22=13>>13 pounds. #### 13 A new movie gets released and makes $120 million in the box office for its opening weekend. It ends up making 3.5 times that much during its entire run. If the production company gets to keep 60%, how much profit did they make if the movie cost $60 million to produce? How much money did the movie make? ** Over the movies run it made 120*3.5=<<120*3.5=420>>420 million How much money did the production company make? ** So the production company made 420,000,000*.6=$<<420000000*.6=252000000>>252,000,000 How much profit did the production company make? ** So they got a profit of 252,000,000-60,000,000=$<<252000000-60000000=192000000>>192,000,000 #### 192000000 Omi is twice as old as Kimiko. Arlette is 3/4 times as old as Kimiko. If Kimiko is 28 years old, calculate the average age of the three? How old is Omi? ** If Kimiko is 28, Omi is 2 * 28 years = <<28*2=56>>56 years old. How old is Arlette? ** Arlette is 3/4 * 28 years = <<3/4*28=21>>21 years old. How old are the three? ** If you add up their ages, it sums to 21 years + 56 years + 28 years = <<21+56+28=105>>105 years What is the average age of the three? ** The average age for the three is 105 years / 3 people = <<105/3=35>>35 years/person #### 35 A hay farmer harvested 560 bales of hay from 5 acres of grass per month last year. This year, he planted an additional 7 acres of grass. If the farmer also owns 9 horses and each horse consumes 3 bales of hay a day, how many bales of hay would the farmer have left by the end of December if he starts feeding them this year's hay beginning the first day of September? How many bales of hay can the farmer harvest from each acre of grass? ** For every acre of grass, the farmer can harvest 560/5 = <<560/5=112>>112 bales of hay each month. How many acres of grass does the farmer have? ** This year, the farmer has 7 + 5 = <<7+5=12>>12 acres of grass. How many bales of hay can the farmer harvest from all of his acres of grass? ** He can expect to harvest 12 x 112 = <<12*112=1344>>1344 bales of hay per month. How many bales of hay will the farmer produce this year? ** The total hay production this year is 1344*12 = <<1344*12=16128>>16128 How many days would the farmer have to feed his horses? ** From September to December, the farmer would have to feed his horses for a total of 30 + 31 + 30 + 31 = <<30+31+30+31=122>>122 days How many bales of hay does each horse eat in a day? ** Each day his horse eats a total of 3*9 = <<3*9=27>>27 bales of hay. How many bales of hay will the horses eat in total? ** For the 122 days, the horses will eat a total of 27*122 = <<27*122=3294>>3294 bales. How many bales of hay will the farmer have left by the end of December? ** The total number of bales remaining will be 16128-3294 = <<16128-3294=12834>>12834. #### 12834 A river is to be used for a boat race. If each boat is 3 feet across and they must have at least 2 feet between them or the riverbank, how many boats can race in a river that is 42 feet across? How many feet does each boat take up? ** Each boat will require 3 feet across to fit itself and 2 feet space on one side for a total of 2+3 = <<3+2=5>>5 feet per boat How many feet are left? ** The last boat will need an additional 2 feet space on its other side, so this 2 feet should be subtracted first from the 42 feet which leaves 42-2 = <<42-2=40>>40 feet How many boats can race in a river that is 40 feet across? ** 5 feet per boat on the remaining 40 feet for a total of 40/5 = <<40/5=8>>8 boats #### 8 Joseph and his friends watched two movies in his house. The first movie is 1 hour and 30 minutes long while the second movie is 30 minutes longer than the first. Before the movies, they spent 10 minutes making popcorn and twice as long making fries. How long, in hours, did it take Joseph and his friends to cook and watch the movies? How long was the first movie? ** The first movie was 60 + 30 = <<60+30=90>>90 minutes long since an hour has 60 minutes. How long was the second movie? ** The second movie was 90 + 30 = <<90+30=120>>120 minutes long. How long did it take them to watch the two movies? ** It took them a total of 90 + 120 = <<90+120=210>>210 minutes to watch the two movies. How long did it take them to cook the fries? ** It took them 10 x 2 = <<10*2=20>>20 minutes to cook the fries. How long did it take them to cook? ** Thus, it took them a total of 10 + 20 = <<10+20=30>>30 minutes to cook. How long did it take Joseph and his friends to cook and watch the movies? ** So, they spent 210 + 30 = <<210+30=240>>240 minutes watching the movies and cooking. How long, in hours, did it take Joseph and his friends to cook and watch the movies? ** In hours, this is equal to 240/60 = <<240/60=4>>4 hours. #### 4