Chris’s internet bill is $45 per month for 100 GB and $0.25 for every 1 GB over. His bill for this month is $65. How many GB over was Chris charged for on this bill?

Define a variable ** Let G stand for the number of GB billed, so the total bill is $0.25G + $45 flat rate charge = $65 total bill.

Simplify ** Now we will solve for G. $0.25G + $45 flat rate - $45 = $65 -$45. This simplifies to $0.25G = $20

Simplify ** $0.25G/$0.25 = $20/$0.25

How many GB over was Chris charged for on this bill? ** G = 80 GB were charged on this bill.

#### 80

Rex is taking lessons for his driver’s license. He wants to take 40 hour-long lessons before his test, and decides to have two-hour sessions twice a week until he has done his test. After 6 weeks, how many more weeks will Rex need to continue taking lessons to reach his goal?

How many lessons does Rex take each week? ** Each week, Rex is taking 2 hour-long lessons * 2 times a week =

<<2*2=4>>4 lessons. How many lessons has Rex done after 6 weeks? ** After 6 weeks, he has done 4 lessons per week * 6 weeks = <<4*6=24>>24 lessons. How many more lessons does Rex need to take? ** So Rex still needs 40 total lessons – 24 lessons taken = <<40-24=16>>16 lessons. How many more weeks will Rex need to continue taking lessons to reach his goal? ** He will therefore need lessons for another 16 lessons / 4 lessons per week = <<16/4=4>>4 weeks. #### 4 Layla is feeding her pet fish. She has two Goldfish which each get one teaspoon of fish food. Her 3 Swordtails each get 2 teaspoons of food. Her 8 Guppies each eat half a teaspoon of food. How much food does she have to give to her fish in total? How many teaspoons of food do the Goldfish eat? ** The two Goldfish eat a total of 2 * 1 = <<2*1=2>>2 teaspoons of food. How many teaspoons of food do the Swordtails eat? ** The 3 Swordtails eat a total of 3 * 2 = <<3*2=6>>6 teaspoons of food. How many teaspoons of food do the Guppies eat? ** The 8 Guppies eat a total of 8 * 1/2 = <<8*1/2=4>>4 teaspoons of food. How many teaspoons of food do all of her fish eat? ** In total, all of her fish eat 2 + 6 + 4 = <<2+6+4=12>>12 teaspoons of fish food. #### 12 James had two browsers on his computer. In each browser, he opened three windows, each with ten tabs. What's the total number of tabs he opened in all the browsers together? How many tabs are in each window? ** The total number of tabs in three windows of each browser is 10*3 = <<10*3=30>>30 tabs. How many tabs are in the two browsers together? ** If James had two browsers on his computer and in each browser he opened three windows, the total number of tabs in the two browsers is 2*30 = <<2*30=60>>60 tabs. #### 60 It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude and 3 eggs from Blanche. Nancy laid 2 eggs as did Martha. On the way, he dropped 2 eggs. How many eggs did Trevor have left? How many eggs did Trevor collect? ** He collected 4+3+2+2 eggs for a total of <<4+3+2+2=11>>11 eggs. How many eggs did Trevor have left? ** He dropped 2 eggs so 11-2 = <<11-2=9>>9 eggs left #### 9 If I give my brother 2 marbles I will have double his number of marbles, but my friend will have triple the number I do. The total number of marbles we have together is 63. How many marbles do I have? Define a variable ** Let X be the number of marbles I have. How many marbles will I have after giving my brother 2 marbles? ** If I give my brother 2 marbles, I'll have X-2 marbles left. How many marbles will my brother have after giving him 2 marbles? ** And my brother will have (X-2)/2 marbles. How many marbles will my friend have after giving him 2 marbles? ** And my friend will have (X-2)*3 left. Write an equation ** So the total number of marbles is X-2 + (X-2)/2 + (X-2)*3 = 63. Simplify ** (X-2)*9/2 = 63. Simplify ** X-2 = 14. Simplify ** X = <<16=16>>16 marbles. #### 16 The teacher agrees to order pizza for the class. For every student in the class, she will buy 2 pieces of cheese and 1 piece of onion and they will eat exactly that amount. A large pizza has 18 slices. She orders 6 total pizzas and there are 8 pieces of cheese and 4 pieces of onion leftover. How many students are in the class? How many cheese pizzas are purchased? ** Cheese pizzas are 2/3 of the pizza's purchased because 2 / (2+1) = 2/3 How many cheese pizzas are purchased? ** She buys 4 cheese pizzas because 6 x (2/3) = <<6*2/3=4>>4 How many pieces of cheese pizza are purchased? ** These give her 72 pieces of cheese pizza because 4 x 18 = <<4*18=72>>72 How many pieces of cheese pizza are purchased? ** The students at 64 pieces of cheese because 72 - 8 = <<72-8=64>>64 How many students are in the class? ** There are 32 students in her class because 64 / 2 = <<64/2=32>>32 #### 32 Bert bought some unique stamps for his collection. Before the purchase, he had only half the stamps he bought. If he bought 300 stamps, how many stamps does Bert have in total after the purchase? How many stamps did Bert have before the purchase? ** Before the purchase, Bert had 300 * 1/2 = <<300*1/2=150>>150 stamps. How many stamps does Bert have in total after the purchase? ** So after the purchase he has 300 + 150 = <<300+150=450>>450 stamps. #### 450 In seven years, Talia will be 20 years old. Talia's mom is currently three times as old as Talia is today. In three years, Talia's father will be the same age as Talia's mom is today. Currently, how many years old is Talia's father? How old is Talia currently? ** In seven years, Talia will be 20 years old, and therefore Talia is currently 20-7=<<20-7=13>>13 years old. How old is Talia's mom currently? ** Talia's mom is currently three times as old as Talia is today, or 3*13=<<3*13=39>>39 years old. How old is Talia's father currently? ** If in three years, Talia's father will be the same age as Talia's mom is today, then Talia's father is currently 39-3=<<39-3=36>>36 years old. #### 36 Louise is hanging 30 of her pictures on the wall. She hangs some of them vertically, half of them horizontally, then hangs the remaining 5 pictures haphazardly. How many pictures did Louise hang vertically? How many pictures are hanging horizontally? ** There are 30 / 2 = <<30/2=15>>15 pictures hanging horizontally. How many pictures are hanging either horizontally or haphazardly? ** So there is a total of 15 + 5 = <<15+5=20>>20 pictures hanging either horizontally or haphazardly. How many pictures are hanging vertically? ** Therefore, there are 30 – 20 = <<30-20=10>>10 pictures hanging vertically. #### 10