Pete walks backwards three times faster than Susan walks forwards, and Tracy does one-handed cartwheels twice as fast as Susan walks forwards. But Pete can walk on his hands only one quarter the speed that Tracy can do cartwheels. If Pete walks on his hands at 2 miles per hour, how fast can Pete walk backwards, in miles per hour?

How fast can Tracy do 1-handed cartwheels? ** If Pete walks on hands at 1/4 what Tracy can do 1-handed cartwheels, then Tracy can do 1-handed cartwheels at 2*4=8 miles per hour.

How fast does Susan walk? ** Since Tracy does 1-handed cartwheels twice the rate of Susan's forward walking, then Susan walks at 8/2=

<<8/2=4>>4 miles per hour. How fast does Pete walk backwards? ** Pete walks backwards 3x faster than Susan walks forward, and thus Pete walks backwards at 4*3=12 miles per hour. #### 12 James spends 3 hours vacuuming and 3 times as long on the rest of his chores. How long does he spend on his chores? How long does he spend on his other chores? ** He spends 3*3=<<3*3=9>>9 hours on his other chores How long does he spend on chores? ** So he spends 3+9=<<3+9=12>>12 hours on chores #### 12 Gary has 30 grams of gold that cost $15 per gram. Anna has 50 grams of gold for the cost of $20 per gram. How much is the cost of their gold combined? How much does Gary’s gold cost? ** The cost of Gary’s gold is 30 * $15 = $<<30*15=450>>450. How much does Anna’s gold cost? ** The cost of Anna’s gold is 50 * $20 = $<<50*20=1000>>1000. How much is the cost of their gold combined? ** The total cost of their gold is $450 + $1000 = $<<450+1000=1450>>1450. #### 1450 Andy is mixing blue, green and white paint in a 1 : 2 : 5 ratio. If he uses 6 gallons of green paint, how many gallons of paint does he use total? How many gallons of blue paint does Andy use? ** First find the number of gallons of blue paint by multiplying the gallons of green paint by the ratio between the blue and green paint: 1 blue gallon/2 green gallons * 6 gallons = 3 gallons How many gallons of white paint does Andy use? ** Then find the number of gallons of white paint by multiplying the gallons of green paint by the ratio between the white and green paint: 5 white gallons/2 green gallons * 6 gallons = 15 gallons How many gallons of paint does Andy use? ** Then add the number of gallons of each color to find the total number of gallons of paint: 6 gallons + 3 gallons + 15 gallons = <<6+3+15=24>>24 gallons #### 24 There are 14 kindergartners and 24 first graders and some second graders in Ms. Watson's class. Overall Ms. Watson has 42 students. How many second graders are in Ms. Watson’s class? How many kindergartners and first graders are there in total? ** There are 14+24 = <<14+24=38>>38 kindergartners and first graders in Ms. Watson’s class. How many second graders are in Ms. Watson’s class? ** There are 42-38 = <<42-38=4>>4 second graders in Ms. Watson’s class. #### 4 A town is holding a fireworks display for New Year’s Eve. They light enough fireworks to show the full year then light enough fireworks to write “HAPPY NEW YEAR” in the sky. They then light another 50 boxes of fireworks as part of the display. Each box of fireworks contains 8 fireworks. If it takes 6 fireworks to display a number and 5 fireworks to display a letter, how many fireworks are lit during the display? How many fireworks are used to write out the full year? ** Writing out the full year uses 4 numbers so this takes 4 numbers * 6 fireworks per number = <<4*6=24>>24 fireworks. How many fireworks are used to write out “HAPPY NEW YEAR� ** “HAPPY NEW YEAR” contains 12 letters so this takes 12 letters * 5 fireworks per letter = <<12*5=60>>60 fireworks. How many fireworks are lit at the start of the display? ** There is therefore a total of 24 + 60 = <<24+60=84>>84 fireworks lit at the start of the display. How many fireworks are lit from the boxes? ** From the boxes, they lit another 50 boxes * 8 fireworks per box = <<50*8=400>>400 fireworks. How many fireworks are lit in total? ** So in total, the whole display uses 84 + 400 = <<84+400=484>>484 fireworks. #### 484 Jimmy and Irene go shopping for clothes on a Tuesday, where senior citizens get a 10% discount on their purchases. Jimmy picks out 3 shorts from the $15 rack. Irene grabs 5 shirts from the $17 rack. How much money do they give to the cashier? How much do Jimmy’s shorts cost? ** Jimmy’s shorts cost 3 x $15 = $<<3*15=45>>45. How much do Irene’s shirts cost? ** Irene’s shirts cost 5 x $17 = $<<5*17=85>>85. How much do Jimmy and Irene’s clothes cost? ** Total cost for the clothes is $45 + $85 = $<<45+85=130>>130. How much is the 10% discount? ** 10% discount on the clothes is $130 x 10% = $<<130*10*.01=13>>13. How much money do they give to the cashie? ** They give the cashier $130 - $13 = $<<130-13=117>>117. #### 117 To get to an island called "Virgo", Tom needs to travel by plane and then by boat. The plane trip is four times longer than the boat trip, and the boat trip takes up to 2 hours. In how many hours is Tom able to get to the "Virgo" island? How many hours is the plane trip? ** The plane trip is four times longer than the 2-hour long boat trip, which means it takes 4 * 2 = <<4*2=8>>8 hours. How many hours is Tom able to get to the "Virgo" island? ** So in total, the whole journey to "Virgo" islands lasts 8 + 2 = <<8+2=10>>10 hours. #### 10 Lilia has 15 peaches. She sold 10 peaches to her friends for $2 each, while 4 other peaches were sold to her relatives for $1.25 each, and she left the other one for herself. How much did she earn after selling 14 peaches? How much did Lilia earn from selling the peaches to her friends? ** Lilia earned 10 x $2 = $<<10*2=20>>20 for selling the peaches to her friends. How much did Lilia earn from selling the peaches to her relatives? ** She also earned 4 x $1.25 = $<<4*1.25=5>>5 for selling the peaches to her relatives. How much did Lilia earn after selling 14 peaches? ** Therefore, Lilia earned $20 + $5 = $<<20+5=25>>25 for selling 14 peaches. #### 25 There are 12 carpets in house 1, 20 carpets in house 2, and 10 carpets in house 3. If house 4 has twice as many carpets as house 3, how many carpets do all 4 houses have in total? How many carpets does house 4 have? ** House 4 has 2 * 10 house 3 carpets = <<2*10=20>>20 carpets How many carpets are there in total? ** The total number of carpets across all houses is 12 + 20 + 10 + 20 = <<12+20+10+20=62>>62 #### 62