Brennan was researching his school project and had to download files from the internet to his computer to use for reference. After downloading 800 files, he deleted 70% of them because they were not helpful. He downloaded 400 more files but again realized that 3/5 of them were irrelevant. How many valuable files was he left with after deleting the unrelated files he downloaded in the second round?

How many files did Brennan download in the first round? ** The number of non-valuable files Brennan downloaded in the first round is 70/100*800 =

<<70/100*800=560>>560 files. How many files did Brennan download in the first round? ** The number of valuable files Brennan downloaded in the first round is 800-560 = <<800-560=240>>240 How many files did Brennan download in the second round? ** When he downloaded 400 new files, there were 3/5*400= <<3/5*400=240>>240 non-useful files, which he deleted again. How many files did Brennan download in the second round? ** The total number of valuable files he downloaded in the second round is 400-240 = <<400-240=160>>160 How many files did Brennan have after deleting the unrelated files he downloaded in the second round? ** To write his research, Brennan had 160+240 = <<160+240=400>>400 useful files to reference to write his research. #### 400 There are 5 houses on a street, and each of the first four houses has 3 gnomes in the garden. If there are a total of 20 gnomes on the street, how many gnomes does the fifth house have? How many gnomes are in the first four houses? ** In the first four houses, there are a total of 4 houses * 3 gnomes = <<4*3=12>>12 gnomes. How many gnomes does the fifth house have? ** Therefore, the fifth house had 20 total gnomes – 12 gnomes = <<20-12=8>>8 gnomes. #### 8 Mrs. Snyder used to spend 40% of her monthly income on rent and utilities. Her salary was recently increased by $600 so now her rent and utilities only amount to 25% of her monthly income. How much was her previous monthly income? Define a variable ** Let her previous monthly income be p How much was her previous monthly income? ** The cost of her rent and utilities was 40% of p which is (40/100)*p = 2p/5 How much was her previous monthly income? ** Her income was increased by $600 so it is now p+$600 How much was her previous monthly income? ** The cost of her rent and utilities now amount to 25% of (p+$600) which is (25/100)*(p+$600) = (p+$600)/4 How much was her previous monthly income? ** Equating both expressions for cost of rent and utilities: 2p/5 = (p+$600)/4 How much was her previous monthly income? ** Multiplying both sides of the equation by 20 gives 8p = 5p+$3000 How much was her previous monthly income? ** Subtracting 5p from both sides gives: 3p = $3000 How much was her previous monthly income? ** Dividing both sides by 3 gives p = $1000 #### 1000 Ann, Bill, Cate, and Dale each buy personal pan pizzas cut into 4 pieces. If Bill and Dale eat 50% of their pizzas and Ann and Cate eat 75% of the pizzas, how many pizza pieces are left uneaten? How many pizza pieces are there in total? ** In total, there are 4 x 4 = <<4*4=16>>16 pizza pieces. How many pieces do Bill and Dale eat? ** Bill and Dale eat 2 x 4 x 50% = <<2*4*50*.01=4>>4 pieces. How many pieces do Ann and Cate eat? ** Ann and Cate eat 2 x 4 x 75% = <<2*4*75*.01=6>>6 pieces. How many pieces do Bill, Dale, Ann, and Cate eat? ** The four of them eat 4 + 6 = <<4+6=10>>10 pieces. How many pizza pieces are left uneaten? ** There are 16 - 10 = <<16-10=6>>6 pizza pieces uneaten. #### 6 Noah is a painter. He paints pictures and sells them at the park. He charges $60 for a large painting and $30 for a small painting. Last month he sold eight large paintings and four small paintings. If he sold twice as much this month, how much is his sales for this month? How much did Noah earn from the large paintings? ** Noah earned $60/large painting x 8 large paintings = $<<60*8=480>>480 for the large paintings. How much did Noah earn from the small paintings? ** He also earned $30/small painting x 4 small paintings = $<<30*4=120>>120 for the small paintings. How much did Noah earn last month? ** His total sales last month were $480 + $120 = $<<480+120=600>>600. How much will Noah sell this month? ** So, his sales this month are $600 x 2 = $<<600*2=1200>>1200. #### 1200 A car is driving through a tunnel with many turns. After a while, the car must travel through a ring that requires a total of 4 right-hand turns. After the 1st turn, it travels 5 meters. After the 2nd turn, it travels 8 meters. After the 3rd turn, it travels a little further and at the 4th turn, it immediately exits the tunnel. If the car has driven a total of 23 meters around the ring, how far did it have to travel after the 3rd turn? How far has the car traveled around the ring? ** From the details given, the car has traveled 5 meters at the 1st turn + 8 meters after the 2nd turn + 0 meters after the 4th turn = <<5+8+0=13>>13 meters around the ring. How far did the car have to travel after the 3rd turn? ** It must therefore have driven 23 total meters – 13 calculated meters = 10 meters after the 3rd turn. #### 10 To make pizza, together with other ingredients, Kimber needs 10 cups of water, 16 cups of flour, and 1/2 times as many teaspoons of salt as the number of cups of flour. Calculate the combined total number of cups of water, flour, and teaspoons of salt that she needs to make the pizza. How many teaspoons of salt does Kimber need? ** To make the pizza, Kimber half as many teaspoons of salt as the number of cups of flour, meaning she needs 1/2*16 = <<16*1/2=8>>8 teaspoons of salt. How many cups of flour and teaspoons of salt does Kimber need? ** The total number of cups of flour and teaspoons of salt she needs is 8+16 = <<8+16=24>>24 How many cups of water, flour, and salt does Kimber need? ** She also needs 10 cups of water, which means the total number of cups of water and flour and teaspoons of salt she needs is 24+10 = <<24+10=34>>34 #### 34 Mr. Sam shared a certain amount of money between his two sons, Ken and Tony. If Ken got $1750, and Tony got twice as much as Ken, how much was the money shared? How much did Tony get? ** Tony got twice $1750 which is 2*$1750 = $<<2*1750=3500>>3500 How much was the money shared? ** The total amount shared was $1750+$3500 = $<<1750+3500=5250>>5250 #### 5250 Mr. Sanchez found out that 40% of his Grade 5 students got a final grade below B. How many of his students got a final grade of B and above if he has 60 students in Grade 5? How many of his students got B and above? ** Since 40% of his students got below B, 100% - 40% = 60% of Mr. Sanchez's students got B and above. How many of his students got B and above? ** Thus, 60 x 60/100 = <<60*60/100=36>>36 students got B and above in their final grade. #### 36 Lisa, Jack, and Tommy earned $60 from washing cars all week. However, half of the $60 was earned by Lisa. Tommy earned half of what Lisa earned. How much more money did Lisa earn than Tommy? How much money did Lisa earn? ** Lisa earned $60 * 1/2 = $<<60*1/2=30>>30. How much money did Tommy earn? ** Tommy earned $30 * 1/2 = $<<30*1/2=15>>15. How much more money did Lisa earn than Tommy? ** Lisa earned $30 - $15 = $<<30-15=15>>15 more than Tommy. #### 15