Carson is refilling his tires. Each tire can hold 500 cubic inches of air. Two of the tires are completely flat and empty. One tire is 40% full and the last tire is 70% full. If Carson injects 50 cubic inches of air with each pump, how many pumps will it take him to fill all the tires?

How many cubic inches are in two empty tires? ** First, if the a full tire needs 500 cubic inches of air, then two empty tires need: 500 cubic inches/tire * 2 tires =

<<500*2=1000>>1000 cubic inches. How many cubic inches is the 40%-full tire? ** Accordingly, the 40%-full tire needs 500 cubic inches * (100%-40%). How many cubic inches is the 40%-full tire? ** So, we find the 40%-full tire needs 500 cubic inches * (60%) = <<500*(60*.01)=300>>300 cubic inches. How many cubic inches is the 70%-full tire? ** And, the 70%-full tire needs 500 cubic inches * (100%-70%). How many cubic inches is the 70%-full tire? ** So, the 70%-full tire needs 500 cubic inches * (30%)= <<500*(30*.01)=150>>150 cubic inches. How many cubic inches are in all the tires? ** Now add up the needs of all the tires to find the total number of cubic inches needed: 1000 cubic inches + 300 cubic inches + 150 cubic inches = <<1000+300+150=1450>>1450 cubic inches. How many pumps will it take him to fill all the tires? ** Finally, if the pumps each hold 50 cubic inches, the total number of pumps needed is 1550 cubic inches / 50 cubic inches/pump = 29 pumps. #### 29 Joel is picking peppers from his garden. He picks 7 on Sunday, 12 on Monday, 14 on Tuesday, 12 on Wednesday, 5 on Thursday, 18 on Friday and 12 on Saturday. He knows that in his garden 20% of the peppers are hot and the rest are not. How many non-hot peppers did he pick? How many peppers did Joel pick? ** He picked 80 peppers because 7 + 12 + 14 + 12 + 5 + 18 + 12 = <<7+12+14+12+5+18+12=80>>80 How many peppers are not hot? ** 80% of the peppers are not hot because 100 - 20 = <<100-20=80>>80 How many non-hot peppers did Joel pick? ** He picked 64 non-hot peppers because 80 x .8 = <<80*.8=64>>64 #### 64 Teresa orders 2 fancy ham and cheese sandwiches for $7.75 each at a local shop. While there, she decides to pick up some salami for $4.00, more brie which is three times the price of the salami, a 1/4 pound of olives that are $10.00 per pound, 1/2 pound of feta cheese that’s $8.00 a pound and another loaf of french bread that is $2.00. How much does she spend at the local shop? How much do the sandwiches cost? ** She orders 2 sandwiches that are $7.75 so they cost 2*$7.75 = $<<2*7.75=15.50>>15.50 How much does the brie cost? ** The brie is three times more expensive than the $4.00 salami so the brie costs 3*$4 = $<<3*4=12.00>>12.00 How much do the olives cost? ** She buys 1/4 pound of the olives that costs $10.00 a pound so they cost .25*$10 =$<<1/4*10=2.50>>2.50 How much does the feta cost? ** She buys 1/2 pound of feta that costs $8.00 a pound so it costs .5*$8 = $<<1/2*8=4.00>>4.00 How much does Teresa spend at the local shop? ** The salami is $4.00, the brie is $12.00, olives are $2.50 and the feta is $4.00 and the sandwiches are $15.50 for a total of $4+$12+$2.50+$4+$15.50 = $<<4+12+2.5+4+15.50=38.00>>38.00 How much does Teresa spend at the local shop? ** Adding the french bread gives $38.00+$2.00 = $<<38+2=40>>40 #### 40 Nida has 50 chocolates in which some are in 3 filled boxes and 5 pieces are not in a box. Her friend brought 25 pieces of chocolates. If all chocolates must be placed in a box, how many more boxes do they need? How many chocolates are in the three boxes? ** There are 50 - 5 = <<50-5=45>>45 chocolates in three boxes. How many chocolates are in each box? ** So, each box is filled with 45/3 = <<45/3=15>>15 chocolates. How many chocolates are needed to be placed in boxes? ** 5 + 25 = <<5+25=30>>30 chocolates are needed to be placed in boxes. How many boxes do they need? ** Hence, they needed 30/15 = <<30/15=2>>2 boxes for the 30 chocolates. #### 2 There are 24 students in the class. One-third had their school portraits taken before lunch. After lunch, but before gym class, 10 additional students had their portraits taken. After gym class, how many students have not yet had their picture taken? How many students were photographed before lunch? ** Before lunch, 24/3=<<24/3=8>>8 students were photographed. How many students have been photographed by gym class? ** Then 8+10=<<8+10=18>>18 have been photographed by gym class. How many students remain? ** So 24-18=<<24-18=6>>6 remain. #### 6 A captain steers his ship 100 miles north on the first day of their journey. On the second day, he sails to the east three times as far as the distance as he covered on the first day. On the third day, the ship travels further east for 110 more miles than the distance it covered on the second day. What is the total distance the ship has traveled in the three days? How far did the ship sail to the east on the second day? ** If the ship traveled 100 miles to the north, it sailed for a distance of 3 * 100 miles = 300 miles to the east on the second day. How far did the ship sail to the east on the third day? ** On the third day, the sheep sailed for 300 miles + 110 miles = <<300+110=410>>410 miles. What is the total distance the ship has traveled in the three days? ** The distance covered by the ship in the three days is 410 miles + 300 miles + 100 miles = <<410+300+100=810>>810 miles #### 810 Gerald thought it would be funny to trick his coworker, who's allergic to peanuts, into eating a peanut butter cookie. When his coworker goes into anaphylactic shock and is taken to the hospital, Gerald is arrested. The judge sentences Gerald to 3 months for assault and 2 years for poisoning, then extends his sentence by 1/3 since this is Gerald's third offense. How many months does Gerald spend in jail? How many months is the 2-year sentence? ** First convert the 2-year sentence to months: 2 years * 12 months/year = <<2*12=24>>24 months How many months is the total sentence? ** Then add the 3 months for assault: 24 months + 3 months = <<24+3=27>>27 months How many months is the 1/3 extension? ** Then find how long the 1/3 extension is: 27 months / 3 = <<27/3=9>>9 months How many months does Gerald spend in jail? ** Finally, add up the three lengths of time to find the total sentence length: 27 months + 9 months = <<27+9=36>>36 months #### 36 Five food companies sponsored a local food bank. Foster Farms donated 45 dressed chickens; American Summits donated twice the number of bottled water than the number of dressed chicken donated by Foster Farms; Hormel donated three times the number of dressed chickens that Foster Farms donated; Boudin Butchers donated one-third of the number of dressed chickens that Hormel donated; Del Monte Foods donated 30 fewer bottles of water than American Summits. How many food items did the companies donate in total? How many bottled waters did American Summits donate? ** American Summits donated 45 x 2 = <<45*2=90>>90 bottled waters. How many spams did Hormel donate? ** Hormel donated 45 x 3 = <<45*3=135>>135 spams. How many sourdoughs did Boudin Bakery donate? ** Boudin Bakery donated 135 x 1/3 = <<135*1/3=45>>45 sourdoughs. How many canned fruits did Del Monte Foods donate? ** Del Monte Foods donated 90 - 30 = <<90-30=60>>60 canned fruits. How many different food items did the companies donate in total? ** Therefore, a total of 45 + 90 + 135 + 45 + 60 = <<45+90+135+45+60=375>>375 different food. #### 375 Tom's cat needs an expensive surgery. He has had pet insurance for 24 months that cost $20 per month. The procedure cost $5000 but the insurance covers all but 20% of this. How much money did he save by having insurance? How much did the insurance cost? ** The insurance cost 24*20=$<<24*20=480>>480 How much did the procedure cost? ** With insurance he pays 5000*.2=$<<5000*.2=1000>>1000 for the procedure How much did he pay? ** So he paid 1000+480=$<<1000+480=1480>>1480 How much money did he save by having insurance? ** So he saved 5000-1480=$<<5000-1480=3520>>3520 #### 3520 Miriam is trying to exercise more and figures if she counts her exercises it will be encouraging to see her numbers go up. On Monday she does 5 push-ups. On Tuesday she does 7 push-ups. On Wednesday she does twice as many push-ups as the day before. On Thursday she does half the number of total pushups she already did that week. Finally, on Friday she does as many pushups as the total number she did over the previous four days. How many pushups does Miriam do on Friday? How many push-ups does Miriam do on Monday and Tuesday? ** On Monday Miriam does 5 push-ups + 7 push-ups on Tuesday = <<5+7=12>>12 push-ups on both days. How many push-ups does Miriam do on Wednesday? ** On Wednesday she does twice as many push-ups as she did on Tuesday, 7 x 2 = <<7*2=14>>14 push-ups on Wednesday. How many pushups did Miriam do over the first 3 days? ** Over the first 3 days, she did a total of 14 + 12 = <<14+12=26>>26 pushups How many pushups did Miriam do on Thursday? ** On Thursday Miriam did 1/2 the same number of total pushups she had already done that week, so she did 1/2 x 26 = <<1/2*26=13>>13 pushups on Thursday. How many push-ups does Miriam do on Friday? ** On Friday she does as many push-ups as the total of what she had done over the previous four days, so she did 5 + 7 + 14 + 13 = <<5+7+14+13=39>>39 push-ups on Friday. #### 39