An entrepreneur is crowdfunding a new business effort. He has three different dollar amount levels of financial backing options and each level is ten times as high as the previous one. He needs to raise $12000 to get his business off the ground. He succeeded after getting two backers at the highest level of financial backing, three at the second level, and ten at the lowest level. How many dollars was the highest level of financial backing?

Define a variable ** Let L represent the lowest level of financial backing.

How many dollars was the second level of financial backing? ** Thus, the second level is 10L and the highest level is 10 * 10L = 100L.

Write an equation ** The entrepreneur got 2 highest level backers, 3 second level backers, and 10 lowest level backers, so 2 * 100L + 3 * 10L + 10L = 200L + 30L + 10L = 240L = $12000.

How many dollars was the lowest level of financial backing? ** Therefore, the lowest level of financial backing was L = 12000 / 240 = $

<<12000/240=50>>50. How many dollars was the highest level of financial backing? ** Thus, the highest level of financial backing was 10 * 10 * 50 = $<<10*10*50=5000>>5000. #### 5000 Tamara is 3 times Kim's height less 4 inches. Tamara and Kim have a combined height of 92 inches. How many inches tall is Tamara? Define a variable ** Let K = Kim's height How tall is Tamara? ** Tamara = 3K - 4 Write an equation ** K + 3K - 4 = 92 Simplify ** 4K - 4 = 92 Simplify ** 4K = 96 How tall is Kim? ** Kim = <<24=24>>24 inches How tall is Tamara? ** Tamara = (3 * 24) - 4 = <<(3*24)-4=68>>68 inches How many inches tall is Tamara? ** Tamara is 68 inches tall. #### 68 A high school bowling team's 3 members scored a total of 810 points in their first match. The first bowler scored 1/3 as many points as the second, and the second bowler scored 3 times as high as the third bowler. How many points did the third bowler score? Define a variable ** Let x represent the score of the third bowler How many points did Bowler 2 score? ** Bowler 2:3x How many points did Bowler 1 score? ** Bowler 1:3x(1/3)=x Write an equation ** Total:x+3x+x=810 Combine like terms ** 5x=810 Divide by 5 ** x=<<162=162>>162 points #### 162 Hannah comes home from work to find her older son taped her younger son to a chair with 22 strands of duct tape. If Hannah can cut 8 strands per minute and her son can cut 3 strands per minute, how long will it take them to free her younger son? How many strands can Hannah and her son cut per minute? ** First find the total number of strands the two of them can cut per minute: 8 strands + 3 strands = <<8+3=11>>11 strands How many minutes does it take to cut all the strands? ** Then divide the total number of strands by the number of strands they cut per minute to find the number of minutes it takes to cut all the strands: 22 strands / 11 strands/minute = <<22/11=2>>2 minutes #### 2 Natalie's father has saved up $10,000 to split up between his kids. Natalie will get half, as she is the oldest. Rick will get 60 percent of the remaining money, and Lucy will get whatever is left after Natilie and Rick get paid. How much money does Lucy get? How much money will Natalie get? ** Natalie: 10000/2=<<10000/2=5000>>5000$ How much money is left? ** 10000-5000=<<10000-5000=5000>>5000 How much money will Rick get? ** Rick:5000(.60)=3000$ How much money will Lucy get? ** 5000-3000=<<5000-3000=2000>>2000$ left for Lucy. #### 2000 Micah can type 20 words per minute and Isaiah can type 40 words per minute. How many more words can Isaiah type than Micah in an hour? How many minutes are in an hour? ** There are 60 minutes in an hour. How many words can Micah type in an hour? ** Micah can type 20 x 60 = <<20*60=1200>>1200 words in an hour. How many words can Isaiah type in an hour? ** Isaiah can type 40 x 60 = <<2400=2400>>2400 words in an hour. How many more words can Isaiah type than Micah in an hour? ** Isaiah can type 2400 - 1200 = <<2400-1200=1200>>1200 words more than Micah in an hour. #### 1200 Jose bought 20,000 square meters of land and needs to divide it equally with his four siblings. How much land, in the square meters, will Jose have after dividing it with his siblings? How many pieces will the land be divided into? ** The land will be divided into 1 (Jose) + 4 siblings = <<1+4=5>>5 pieces. How much land will Jose have after dividing it with his siblings? ** So, Jose will have 20,000/5 = <<20000/5=4000>>4000 square meters of land. #### 4000 Darla has 6 books in her locker. Katie has half as many books as Darla, and Gary has 5 times the number of books that Darla and Katie have combined. How many books do the three have total? How many books does Darla have? ** Darla:6 books How many books does Katie have? ** Katie:6/2=<<6/2=3>>3 books How many books does Gary have? ** Gary: 5(6+3)=45 books How many books do the three have total? ** 6+3+45=<<6+3+45=54>>54 books #### 54 A farmer owns a hog that recently gave birth to 6 piglets. If the farmer raises the piglets until they are fully grown, he can sell the fully grown pig for $300. Each piglet must grow for at least 12 months before it is large enough to be sold. It costs the farmer $10 per month to feed each animal until it is sold. If the farmer sells 3 pigs after 12 months, and the remaining 3 pigs after 16 months, how much profit did he earn in total (after deducting the cost of food)? How much will the 3 pigs sold after 12 months cost the farmer in food costs? ** The 3 pigs that are sold after 12 months will cost the farmer 12*10*3 = $<<12*10*3=360>>360 in food costs. How much will the 3 pigs sold after 16 months cost the farmer in food costs? ** The 3 pigs that are sold after 16 months will cost the farmer 16*10*3 = $<<16*10*3=480>>480 in food costs. How much did the farmer spend on food? ** Thus, the total food cost to raise the 6 piglets was 360 + 480 = $<<360+480=840>>840. How much will the 6 fully grown pigs sell for? ** Next, selling the 6 fully grown pigs will earn the farmer 6*300 = $<<6*300=1800>>1800 in revenue. How much profit did the farmer earn? ** Therefore, the earn the farmer 1800 - 840 = $<<1800-840=960>>960 in profit from these sales. #### 960 Bronson decides to collect Oak Leaves from around his Neighborhood. He collects 12 on Thursday and 13 on Friday. 20% are Brown and 20% are Green. The rest are yellow. How many yellow leaves does he collect? How many leaves does Bronson collect? ** He collects 25 leaves because 12 + 13 = <<12+13=25>>25 How many yellow leaves does Bronson collect? ** 60% of them are yellow because 100 - 20 - 20 = <<100-20-20=60>>60 How many yellow leaves does Bronson collect? ** He collects 15 yellow leaves because 25 x .6 = <<25*.6=15>>15 #### 15