On Mary's birthday, her brother surprised her with $100. She spent a quarter of it on a new video game and then used a fifth of what was left on swimming goggles. How much money did she have left?

How much did Mary spend on a new video game? ** Mary spent 100/4=

<<100/4=25>>25 dollars on a new video game. How much money did Mary have left after the video game purchase? ** So, after the video game purchase, Mary was left with 100 - 25 = <<100-25=75>>75 dollars. How much did Mary spend on swimming goggles? ** Mary then bought swimming goggles for 75/5 = <<75/5=15>>15 dollars How much money did Mary have left? ** Mary had 75 - 15 = <<75-15=60>>60 dollars left #### 60 Paul is a chicken trader. One week he had 80 chickens in total to sell at the market. Before he left the farm, he sold his neighbor 12 chickens. At the gate, before the market opens, he got a quick customer and sold another 25 chickens. How many chickens was Paul left with to sell at the market? How many chickens did Paul sell before the market opened? ** Before the market opened, Paul sold 12 + 25 = <<12+25=37>>37 chickens How many chickens was Paul left with to sell at the market? ** So he had 80 - 37 = <<80-37=43>>43 chickens left to sell at the market. #### 43 Frank and his friends Betty and Bill went to their farm and picked oranges to eat. Betty picked 15 oranges and Bill picked 12 oranges. Frank picked three times the number that Betty and Bill picked combined. Frank then planted 2 seeds from each of his oranges into the ground and waited 20 years for each seed to turn into a beautiful orange tree. If each orange tree contains 5 oranges for Frank's son Philip to pick, how many oranges are there for Philip to pick in total? How many oranges did Betty and Bill pick together? ** Together, Betty and Bill picked 15 + 12 = <<15+12=27>>27 oranges. How many oranges did Frank pick? ** Frank picked 3 * 27 = <<3*27=81>>81 oranges. How many orange trees are there 20 years later? ** Frank planted 2 * 81 = <<2*81=162>>162 seeds in total, so there are 162 orange trees 20 years later. How many oranges can Philip pick? ** Philip can then pick 162 * 5 = <<162*5=810>>810 oranges. #### 810 Shannon bought 5 pints of frozen yogurt, two packs of chewing gum, and five trays of jumbo shrimp from The Food Place for a total of $55 If the price of a tray of jumbo shrimp is $5 and a pack of chewing gum costs half as much as a pint of frozen yogurt, what is the price of a pint of frozen yogurt? How much do the trays of jumbo shrimp cost? ** 5 trays of jumbo shrimp cost 5 x 5 = $<<5*5=25>>25 How much do the pints of frozen yogurt and the packs of gum cost in total? ** 5 pints of frozen yogurt and 2 packs of gum in total cost 55 - 25 = $30. How much do the packs of gum cost? ** 2 packs of gum cost as much 2 / 2 = <<2/2=1>>1 pint of frozen yogurt How much does 5 + 1 pints of frozen yogurt cost? ** Therefore 5 + 1 = <<5+1=6>>6 pints of frozen yogurt costs $30. How much does a pint of frozen yogurt cost? ** A pint of frozen yogurt costs 30 / 6 = $<<30/6=5>>5 #### 5 Darrel is an experienced tracker. He can tell a lot about an animal by the footprints it leaves behind. One day he saw a set of coyote footprints. Based on the impressions, he could tell the animal was traveling east at 15 miles per hour, and that the animal left the prints 1 hour ago. If the coyote continues to travel east at 15 miles per hour, and Darrell hops on his motorbike and travels east at 30 miles per hour, how long, in hours, will it take for Darrel to catch up to the coyote? Define a variable ** If we let x be the amount of time, in hours, it will take for Darrel to catch up to the coyote, then we can figure this out. How far does Darrel travel? ** Because the distance Darrel travels is defined as the length of time Darrel travels (x) and Darrel's speed (20mph), or the expression 2*x. How far does the coyote travel? ** And the distance the coyote travels is defined as the length of time the coyote travels (x+1 hour) and the coyote's speed (15 mph), or the expression (x+1)*1. Write an equation ** And since the distance Darrel and the coyote travel is the same, then 2*x=(x+1)*1 Simplify ** Simplifying the expression, we get 2*x=x+1. How long, in hours, will it take for Darrel to catch up to the coyote? ** If we subtract 1 x from each side, we get x=1, the amount of time in hours. #### 1 Xavier runs three times as many miles as Katie, who runs 4 times as many miles as Cole. If Xavier runs 84 miles, how many miles does Cole run? How many miles does Katie run? ** Katie runs one-third of Xavier's distance, which is 84/3 miles = <<84/3=28>>28 miles. How many miles does Cole run? ** Cole runs a quarter of Katie's distance, which translates to 28/4 = <<28/4=7>>7 miles. #### 7 Ginger owns a flower shop, where she sells roses, lilacs, and gardenias. On Tuesday, she sold three times more roses than lilacs, and half as many gardenias as lilacs. If she sold 10 lilacs, what is the total number of flowers sold on Tuesday? How many roses were sold? ** With 10 lilacs sold, three times more roses than lilacs is 3*10=<<10*3=30>>30 roses. How many gardenias were sold? ** Half as many gardenias as lilacs is 10/2=<<10/2=5>>5 gardenias. How many flowers were sold on Tuesday? ** In total, there were 10+30+5=<<10+30+5=45>>45 flowers sold on Tuesday. #### 45 A farm has 5 less than 9 times the amount of hens as roosters. If there are 75 total chickens, how many hens are there? Define a variable ** Let x represent the number of roosters How many hens are there? ** Number of hens:9x-5 Write an equation ** Total:9x-5+x=75 Combine like terms ** 10x-5=75 Add 5 to each side ** 10x=80 Divide by 10 ** x=<<8=8>>8 How many hens are there? ** Number of hens: 9(8)-5=67 #### 67 There are 100 lions in Londolozi at first. If lion cubs are born at the rate of 5 per month and lions die at the rate of 1 per month, how many lions will there be in Londolozi after 1 year? What is the change in lions each month? ** There are 5-1=<<5-1=4>>4 more lions each month. How many additional lions will there be after 1 year? ** There will be 4*12=<<4*12=48>>48 more lions after 1 year. How many lions will there be in Londolozi after 1 year? ** There will be 100+48=<<100+48=148>>148 lions in Londolozi after 1 year. #### 148 The lifespan of a hamster is 6 years less than that of a bat. The lifespan of a frog is 4 times that of a hamster. Altogether, the lifespan of the animals is 30 years. What is the lifespan of the bat? How many years does the bat, hamster, and frog have in total? ** Let’s set up an equation by calling the lifespan of a bat x, and therefore the lifespan of the hamster x – 6, and the lifespan of the frog 4 (x – 6) which add together to equal 30, like this: x + x – 6 + 4 (x – 6) = 30. How many years does the bat, hamster, and frog have in total? ** That gives us 6x – 30 = 30 and we should add 30 to each side to try to isolate the x. How many years does the bat, hamster, and frog have in total? ** Now we have 6x = 60, which we will divide by 6, 6x / 6 = 60 / 6. What is the lifespan of the bat? ** This gives us x = <<10=10>>10. The bat has a lifespan of 10 years. #### 10