Javier is an Olympic javelin thrower. In the last Olympics, he threw the javelin three times. The first throw, he threw the javelin twice as far as he threw the javelin on his second throw, but only half as far as he threw it the third throw. If the sum of all three throws was 1050 meters, then how far, in meters, did he throw the javelin on his first throw?

Let x be the distance he threw the javelin on the first throw.

Thus, the sum of his three throws is x+0.5x+2x=1050 meters.

Thus, 3.5x=1050.

And we find the distance he threw the javelin on the first throw is x=

<<300=300>>300 meters. #### 300 Lavinia’s daughter is 10 years younger than Katie’s daughter. Lavinia’s son is 2 times the age of Katie’s daughter. If Katie’s daughter is 12 years old, how many years older is Lavinia’s son than Lavinia’s daughter? Lavinia’s daughter is 12 - 10 = <<12-10=2>>2 years old Lavinia’s son is 12 * 2 = <<12*2=24>>24 years old Lavinia’s son is 24 - 2 = <<24-2=22>>22 years older than Lavinia’s daughter. #### 22 An auto shop has a part that Clark needs for $80. Clark buys 7 of them and got a discount. If Clark only had to pay $439, how much was the discount? Originally the car parts would be a total of 80*7 = <<80*7=560>>560 dollars. Clark got a discount for 560-439 = <<560-439=121>>121 dollars. #### 121 Kylie makes 10 beaded necklaces on Monday and 2 beaded necklaces on Tuesday. Then Kylie makes 5 beaded bracelets and 7 beaded earrings on Wednesday. 20 beads are needed to make one beaded necklace. 10 beads are needed to make one beaded bracelet. 5 beads are needed to make one beaded earring. How many beads does Kylie use in total to make her jewelry? Kylie makes 10 + 2 = <<10+2=12>>12 beaded necklaces The number of beads used for the necklaces is 12 * 20 = <<12*20=240>>240 beads The number of beads used for the bracelets is 5 * 10 = <<5*10=50>>50 beads The number of beads used for the earrings is 7 * 5 = <<7*5=35>>35 beads The total number of beads used is 240 + 50 + 35 = <<240+50+35=325>>325 beads #### 325 Nick has 35 quarters. 2/5 of the quarters are state quarters, and 50 percent of the state quarters are Pennsylvania. How many Pennsylvania state quarters does Nick have? State quarters:35(2/5)=14 quarters Pennsylvania:14(.50)=7 quarters #### 7 Henrietta is repainting her house. The walls in the living room take up 600 square feet. She has three bedrooms. The walls in each bedroom take up 400 square feet. If one gallon of paint can cover 600 square feet, how many gallons of paint does Henrietta need to paint her house? The total square footage from the three bedrooms is 3 * 400 = <<3*400=1200>>1200 square feet. The total square footage of the house is 1200 + 600 = <<1200+600=1800>>1800 square feet Henrietta needs 1800 / 600 = <<1800/600=3>>3 gallons of paint #### 3 The math questions in a contest are divided into three rounds: easy, average, and hard. There are corresponding points given for each round. That is 2, 3, and 5 points for every correct answer in the easy, average, and hard rounds, respectively. Suppose Kim got 6 correct answers in the easy; 2 correct answers in the average; and 4 correct answers in the difficult round, what are her total points in the contest? Kim got 6 points/round x 2 round = <<6*2=12>>12 points in the easy round. She got 2 points/round x 3 rounds = <<2*3=6>>6 points in the average round. She got 4 points/round x 5 rounds = <<4*5=20>>20 points in the difficult round. So her total points is 12 points + 6 points + 20 points = <<12+6+20=38>>38 points. #### 38 The perimeter of a square-shaped piece of paper is 20 cm shorter than the height of a computer screen. How many cm is the height of the screen if the side of the square paper is 20 cm? The perimeter of a square is found by 4*side, which means the square paper has a perimeter of 4*20 = <<4*20=80>>80 Since the perimeter of the square is 20 cm shorter than the height of the computer screen, the height of the computer screen is 20+80 = <<20+80=100>>100cm. #### 100 Tony wants to build the longest rope he possibly can, so he collects all the rope in his home. He finds an 8-foot rope, a 20-foot rope, three 2 foot ropes, and a 7-foot rope. each knot between the ropes makes him lose 1.2 foot per knot. How long is his rope when he's done tying them all together? The combined length of all the rope is 41 feet because 8 + 20 + (2 x 3) + 7 = <<8+20+(2*3)+7=41>>41 He loses 6 feet from the knots because 5 x 1.2 = <<5*1.2=6>>6 The final length is 35 feet because 41 - 6 = <<41-6=35>>35 #### 35 Ben works 8-hour shifts in a furniture shop. It takes him 5 hours to build 1 rocking chair. How many chairs can he build in 10 days? He works 8 hours a day for 10 days means he works 8*10 = <<8*10=80>>80 hours It takes him 5 hours to build one rocking chair so over 80 hours he builds 80/5 = <<80/5=16>>16 rocking chairs #### 16