A psychologist believes one in every four people has a disorder he calls ZYX syndrome. The clinic where he works has recently doubled its previous number of 26 patients. How many patients is the psychologist likely to diagnose with ZYX syndrome?

The clinic has 26 * 2 =

<<26*2=52>>52 patients. The psychologist believes 1/4 of people have the disorder, so he is likely to diagnose 52 / 4 = <<52/4=13>>13 patients with ZYX syndrome. #### 13 Jerry bought 48 firecrackers for the 4th of July. A police officer discovered and confiscated 12 of them. 1/6 of the remaining ones were defective. If Jerry set off half the good firecrackers, how many firecrackers did he set off? First subtract the 12 confiscated firecrackers from the original number: 48 firecrackers - 12 firecrackers = <<48-12=36>>36 firecrackers Then multiply this number by 1/6 to find how many were defective: 36 firecrackers * 1/6 = <<36*1/6=6>>6 firecrackers Then subtract the defective firecrackers to find how many were good: 36 firecrackers - 6 firecrackers = <<36-6=30>>30 firecrackers Then divide this number in half to find how many firecrackers Jerry set off: 30 firecrackers / 2 = <<30/2=15>>15 firecrackers #### 15 A florist is making bouquets for the weekend. The florist uses red, yellow, orange, and purple flowers, and each bouquet contains 9 flowers of any color combinations. This week he planted 125 seeds for each color of flower. Unfortunately, a fungus killed 45 red flowers, 61 yellow, 30 orange, and 40 purple flowers. How many bouquets can the florist make this weekend? There were 125 seeds planted for each of the 4 colors of flower, so there were 125 * 4 = <<125*4=500>>500 flowers planted. The fungus killed 25 red, 31 yellow, 30 orange, and 40 purple flowers, 45 + 61 + 30 + 40 = 176 flowers dead. This leaves 500 - 176 = <<500-176=324>>324 flowers for the bouquets. If the florist puts 9 flowers in each bouquet, he can make 324 / 9 = <<324/9=36>>36 bouquets this weekend. #### 36 Alyssa and Chelsea jointly bought 40 candles to decorate their room. Alyssa used half of them, and Chelsea used 70% of the remaining candles. How many candles are there in the room now? Alyssa used half of the candles, which is 1/2*40 = <<1/2*40=20>>20 candles The number of candles that remained is 40-20 = <<40-20=20>>20 Chelsea used 70% of the remaining candles, a total of 70/100*20 = <<70/100*20=14>>14 candles. The total number of candles in the room now is 40 - 20-14 = <<40-20-14=6>>6 #### 6 Macy and Piper went to the batting cages. Each token gets you 15 pitches. Macy used 11 tokens and Piper used 17. Macy hit the ball 50 times. Piper hit the ball 55 times. How many pitches did Macy and Piper miss altogether? Macy used 11 tokens which are worth 15 pitches each, so 11 tokens x 15 pitches = <<11*15=165>>165 pitches. Piper used 17 tokens x 15 pitches = <<17*15=255>>255 pitches. Together, Macy and Piper received 165 + 255 = <<165+255=420>>420 pitches. Macy hit the ball 50 times + Piper’s 55 hits = <<50+55=105>>105 total hits. Of the 420 pitches – 105 total hits = <<420-105=315>>315 misses. #### 315 Billy is breeding mice for an experiment. He starts with 8 mice, who each have 6 pups. When the pups grow up, all the mice have another 6 pups. Then each adult mouse eats 2 of their pups due to the stress of overcrowding. How many mice are left? First find the number of pups in the first generation: 8 mice * 6 pups/mouse = <<8*6=48>>48 pups Then add the number of adult mice to find the total number of mice: 48 pups + 8 mice = <<48+8=56>>56 mice Then find the number of pups per mouse that survive from the second generation: 6 pups/mouse - 2 pups/mouse = <<6-2=4>>4 pups/mouse Then multiply that number by the number of adult mice to find the number of pups in the second generation: 56 mice * 4 pups/mouse = <<56*4=224>>224 mice Then add the number of adult mice to the number of second-generation pups to find the total number of mice: 224 mice + 56 mice = <<224+56=280>>280 mice #### 280 Five shirts together cost $85. Of the 5 shirts, there are 3 shirts that cost $15 each. If the remaining shirts are each equal in value, what is the cost, in dollars, of one of the remaining shirts? The first 3 shirts cost 15*3=<<15*3=45>>45 dollars in total. There are 5-3=<<5-3=2>>2 shirts remaining. The remaining 2 shirts cost 85-45=<<85-45=40>>40 dollars in total. One of the remaining shirts costs 40/2=<<40/2=20>>20 dollars. #### 20 A pack of dogs found a pile of bones in the dumpster behind the butcher shop. One by one, the dogs crawled into the dumpster, grabbed a mouthful of bones, and ran off with their newfound treasure. In all, there were 5 dogs. The first dog carried off 3 bones. The second dog carried off 1 less bone than the first dog. The third dog carried off twice as many as the second dog. The fourth dog carried off one bone, and the fifth dog carried off twice the number of bones as the fourth dog carried, leaving no remaining bones in the dumpster. How many bones were in the original pile of bones? The second dog carried off 1 less bone than the first dog, or 3-1=<<3-1=2>>2 bones. The third dog carried off twice as many bones as the third dog, or 2*2=<<2*2=4>>4 bones. The fifth dog carried off twice the number of bones as the fourth dog carried, or 2*1=2 bones. Therefore, the original pile of bones contained 3+2+4+1+2=<<3+2+4+1+2=12>>12 bones. #### 12 Kim orders a $10 meal and a drink for 2.5. She gives a 20% tip. She pays with a $20 bill. How much does she get in change? The dinner cost 10+2.5=$<<10+2.5=12.5>>12.5. The tip comes to 12.5*.2=$2.5. So the total cost is 12.5+2.5=$<<12.5+2.5=15>>15. That means she gets 20-15=$<<20-15=5>>5 in change. #### 5 Quentavious has 5 nickels. His friend offers him some gum and will give him two pieces per nickel. If Quentavious leaves with 2 nickels, how many pieces of gum did he get? He spent 3 nickels because 5 - 2 = <<5-2=3>>3 He got 6 pieces of gum because 3 x 2 = <<3*2=6>>6 #### 6