In a dye-making process, a young lady mixes 3/5th of 20 liters of water with 5/6th of 18 liters of vinegar. How many liters of the mixture are obtained?

3/5th of 20 liters of water is 20*(3/5) =

<<20*(3/5)=12>>12 liters 5/6th of 18 liters of vinegar is 18*(5/6) = <<18*(5/6)=15>>15 liters 12 liters of water mixed with 15 liters of vinegar gives 12+15 = <<12+15=27>>27-liter mixture #### 27 Abby is building 2 raised beds to grow vegetables. The beds are both 8 feet long, 4 feet wide and 1 foot high. Each bag of soil has 4 cubic feet. How many bags of soil will she need? One garden bed measures 8ft long, 4ft wide and 1ft high so to find the cubic feet needed, 8*4*1 = <<8*4*1=32>>32 cubic feet of soil needed Both beds are the same size so she needs 2*32 = <<2*32=64>>64 cubic feet of soil Every bag has 4 cubic feet of soil and she needs 64 cubic feet so 64/4 = <<64/4=16>>16 bags needed #### 16 Emmett does 12 jumping jacks, 8 pushups, and 20 situps. What percentage of his exercises were pushups? First find the total number of exercises Emmett does: 12 jumping jacks + 8 pushups + 20 situps = <<12+8+20=40>>40 exercises Then divide the number of pushups by the total number of exercises and multiply by 100% to express the answer as a percentage: 8 pushups / 40 exercises * 100% = 20% #### 20 Bart makes a mixtape. The first side has 6 songs. The second side has 4 songs. Each song is 4 minutes. How long is the total tape? There are 6+4=<<6+4=10>>10 songs on the tape. In total, the time is 10*4=<<10*4=40>>40 minutes. #### 40 Alex needs to be 54 inches tall to ride the newest roller coaster at the theme park. He is 48 inches tall this year. He hears a rumor that for every hour he hangs upside down, he can grow 1/12 of an inch. Normally he grows 1/3 of an inch per month. On average, how many hours does he need to hang upside down each month to be tall enough next year to ride the rollercoaster? He is 6 inches too short this year because 54 - 48 = <<54-48=6>>6 He will naturally grow 4 inches taller because 12 x (1/3) = <<12*(1/3)=4>>4 He needs to grow 2 inches from hanging because 6 - 4 = <<6-4=2>>2 He needs to hang for 24 hours because 2 / (1/12) = <<2/(1/12)=24>>24 He needs to hang for 2 hours a month because 24 / 12 = <<24/12=2>>2 #### 2 The total age of the people in Kaydence's family is 200. If Kaydence's father is 60 years old, Kaydence's mother 2 years younger than Kaydence's father, Kaydence's brother 1/2 the age of Kaydence's father, and Kaydence's sister 40 years old, how old is Kaydence? If Kaydence's father is 60 years old, her mother is 60-2 = <<60-2=58>>58 years old. The total age of the mother and father is 60+58 = <<60+58=118>>118 years Kaydence's brother is half the father's age, which is 1/2*60 =<<1/2*60=30>>30 years. The total age of Kaydence's father, mother, and brother is 30+118= <<30+118=148>>148 years. If you add Kaydence's sister's age to the total age of the father, mother, and brother, you get 148+40 = <<148+40=188>>188 years. If everyone's age in the family is 200, then Kaydence's age is 200-188 = <<200-188=12>>12 years old. #### 12 John builds a toy bridge to support various weights. It needs to support 6 cans of soda that have 12 ounces of soda. The cans weigh 2 ounces empty. He then also adds 2 more empty cans. How much weight must the bridge hold up? The weight of soda was 6*12=<<6*12=72>>72 ounces It had to support the weight of 6+2=<<6+2=8>>8 empty cans The weight of the empty cans is 8*2=<<8*2=16>>16 ounces So it must support 72+16=<<72+16=88>>88 ounces #### 88 Sylvia had one-fifth of incorrect answers in the exam, while Sergio got 4 mistakes. If there were 50 questions, how many more correct answers does Sergio have than Sylvia? Sylvia got 50/5 = <<50/5=10>>10 incorrect answers. This means she got 50 - 10 = <<50-10=40>>40 correct answers. Sergio got 50 - 4 = <<50-4=46>>46 correct answers. So, Sergio got 46 - 40 = <<46-40=6>>6 more correct answers than Sylvia. #### 6 Irene shares half of a small apple with her dog every day. A small apple weighs about 1/4 of a pound. She can currently buy apples for $2.00 a pound. How much will she spend so that she and her dog have enough apples to last for 2 weeks? There are 7 days in a week and she needs apples for 2 weeks so that's 7*2 = <<7*2=14>>14 days She shares an apple with her dog every day so for 14 days so she needs 1*14 = <<1*14=14>>14 apples Each apple weighs 1/4 of a pound and she needs 14 apples so that's .25*14 = <<1/4*14=3.5>>3.5 pounds of apples She needs 3.5 pounds of apples and they are on sale for $2.00 a pound so she will spend 3.5*2 = $<<3.5*2=7.00>>7.00 for apples #### 7 John has a large water collection tank. The tank can hold 200 gallons. It weighs 80 pounds empty. A rainstorm fills it to 80% of capacity. If a gallon of water weighs 8 pounds, how much does it weigh now? The tank has 200*.8=<<200*.8=160>>160 gallons of water in it That water weighs 160*8=<<160*8=1280>>1280 pounds So in total it weighs 1280+80=<<1280+80=1360>>1360 pounds #### 1360