Tim decides to start selling necklaces he makes. He uses 10 charms to make each necklace. Each charm cost $15. He sells the necklace for $200. How much profit does he make if he sells 30?

Each necklace cost 10*15=$

<<10*15=150>>150 to make So he makes a profit of 200-150=$<<200-150=50>>50 each So his total profit is 50*30=$<<50*30=1500>>1500 #### 1500 40 less than 10 times Diaz's age is 20 more than 10 times Sierra's age. If Sierra is currently 30 years old, how old will Diaz be 20 years from now? If Sierra is currently 30 years old, 10 times her age is 30*10 = <<30*10=300>>300. Twenty more than 10 times Sierra's age is 300+20 = 320 320 is 40 less than ten times Diaz's age so 10 times Diaz's age is 320+40 = 360 If ten times Diaz's age is 360, Diaz is 360/10 = <<360/10=36>>36 years old. Twenty years from now, Diaz will be 20+36 = <<20+36=56>>56 years old. #### 56 Candace is trying to decide whether to wear her old shoes or new high-tech shoes for a hike. The high-tech shoes will help Candace walk twice as fast, but they're not broken in yet, so she'll get 1 blister after every 2 hours she spends walking in them. Each blister slows Candance down by 2 miles per hour. If Candance walks 6 miles per hour in the old shoes and plans to hike for 4 hours, how many miles per hour can she go in the new shoes? Wearing the high-tech shoes, Candace can hike 6 mph * 2 = <<6*2=12>>12 mph for the first two hours. Then she gets one blister, so her speed drops to 12 mph - 2 mph = <<12-2=10>>10 mph for the next two hours of the hike. After that time Candace gets another blister, but 2 hours + 2 hours = <<4=4>>4 hours, so the hike is over and we don't care about her speed anymore. Candace spends an equal amount of time walking at 12 mph and 10 mph, so we can average the two speeds to find an overall speed of (12 mph + 10 mph)/2 = <<(12+10)/2=11>>11 mph. #### 11 Charlotte is making a pie. She can't decide if she will make cherry or blueberry. So she decides to make whichever pie is cheapest. Both pies will need $2 for flour, $1 for sugar and $1.5 for eggs and butter to make the crust. The blueberry pie needs 3 pounds of blueberries. The blueberries come in 8 oz containers for $2.25. For the cherry pie, she needs 4 pounds and they come in a four-pound bag for $14. What is the total price to make the cheapest pie? The crust will cost $4.5 because 2 + 1 + 1.5 = <<2+1+1.5=4.5>>4.5 She will need 6 containers for blueberries because 3 x (8/16) = 6 The blueberries will cost $13.5 because 6 x 2.25 = <<6*2.25=13.5>>13.5 The blueberries are cheaper because 13.5 < 14 The blueberry pie will cost $18 to make because 4.5 + 13.5 = <<4.5+13.5=18>>18 #### 18 Paul's grades last semester were very bad. To encourage him, Paul's dad promised him $5 for every B+ he gets in his next scorecard and twice that amount for every A. If Paul obtains at least two A+ he'll double the previous rewards and would receive a flat $15 for every A+ obtained (with no extra bonus). If there are 10 courses with grades in Paul's scorecard, what's the maximum amount he could receive from his dad? We know Paul would get $5 for a B+. However, we know this could be (2x) doubled if he obtains at least two A+. This means 2*$5 = $<<2*5=10>>10 for a B+ if Paul gets at least two A+ We know Paul would get twice the reward of a B+ if he gets an A. This means 2*$5 = $<<5*2=10>>10 for every A However, we know his reward for every A could be (2x) doubled if he obtains at least two A+. This means 2*$10 = $<<2*10=20>>20 for every A if Paul gets at least two A+ We learn here then that Paul will get a higher reward for obtaining A grades ($20) than getting A+ grades ($15) as long as he's able to score at least two A+. To maximize his payout, Paul will need to get only (2) two A+ from his 10 courses. Therefore he should aim to get an A in the remaining 10-2 = <<10-2=8>>8 courses Assuming Paul can get two A+ and eight A in his next scorecard his total payout would be 2*$15 + 8*$20 This translates into $30 + $160 or $<<30+160=190>>190 #### 190 Christine and Janice are having a contest to see who can throw a ball the highest. They each get three throws. On her first throw, Christine throws it 20 feet high. Janice's throw is 4 feet lower than Christine's. On their second throw, Christine throws it ten feet higher than her first throw and Janice throws it twice as high as her first throw. On the final throw, Christine throws it 4 feet higher than her 2nd throw while Janice throws it 17 feet higher than Christine's first throw. What is the height of the highest throw? We know Christine's second throw was 30 feet high because 20 + 10 = <<20+10=30>>30. We know Christine's third throw was 34 feet because 30 + 4 = <<30+4=34>>34. Janice's first throw was 16 feet because 20 - 4 = <<20-4=16>>16. Janice's second throw was 32 feet because 16 * 2 = <<16*2=32>>32. Janice's final throw was 37 feet high because 20 + 17 = <<20+17=37>>37. The six throws were 20 feet, 30 feet, 34 feet, 16 feet, 32 feet, and 37 feet, and of these numbers, 37 feet was the highest. #### 37 TreShaun's full marker has enough ink in it to paint three 4 inch by 4 inch squares. If he colors in two 6 inch by 2 inch rectangles, what percentage of ink is left? Each 4 by 4 square equals 16 square inches because 4 x 4 = <<4*4=16>>16 Three squares equals 48 square inches because 3 x 16 = <<48=48>>48 Each rectangle uses 12 square inches because 2 x 6 = <<2*6=12>>12 Both rectangles will use 24 square inches because 2 x 12 = <<2*12=24>>24 He has 1/2 of the ink left because 24 / 48 = 1/2 He has 50% of the ink left because 1/2 x 100 = <<1/2*100=50>>50 #### 50 In four years, Peter will be twice as old as Harriet. If Peter's age is currently half of his mother's age, who is 60, how old is Harriet now? If Peter's age is currently half of his mother's age, who is 60, Peter is 1/2*60 = <<30=30>>30 years old. In four years, Peter will be 30+4 = <<30+4=34>>34 years old. Since Peter's age in four years will be twice Harriet's age, Harriet will be 34/2 = <<34/2=17>>17 years old in four years. Currently, Harriet is 17-4 = <<17-4=13>>13 years old. #### 13 Janet has 1/3 of a bottle of rose shampoo and 1/4 of a bottle of jasmine shampoo. If she uses 1/12 of a bottle of shampoo per day, how many days will her shampoo last? First cross-multiply to give both fractions the same denominator, then add the fractions: 1/3 + 1/4 = 4/12 + 3/12 Then add these fractions to find that she has 4/12 + 3/12 = 7 /12 of a bottle of shampoo left. Then divide the total amount of shampoo she has by the amount she uses per day to find the number of days the shampoo will last: 7/12 / 1/12/day = 7 days #### 7 There are 45 children in a classroom. One-third of them are girls. How many boys are in the classroom? One-third of all the kids are girls, which means 1/3 * 45 = <<1/3*45=15>>15 children. So there are 45 - 15 = <<45-15=30>>30 boys in the classroom. #### 30