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•  Goods costing 35c per kg are sold at \$420 per tonne. Find the gain as percentage of the cost price. 35c/kg = \$0.35/kg 0.35 × 1000 = \$350/tonne first we must convert to same units 1000kg = 1 tonne gain = 420 – 350 = \$70 find the gain = 70/350 × 100 = 20% to change to percentage gain = gain/original price × 100
•  If the Earth travels through space at a speed of 106,000km/h then the distance travelled by the Earth (in metres) in 30 days in scientific notation is? 106,000 × 24 × 30 = 76,320,000 Distance = speed × time speed = 106,000 time = 30 days which is 30 × 24 hours = 76,320,000 × 1000 = 76,320,000,000m to convert to metres we times the km by 1000 = 7.632 × 1010 m to convert to scientific notation, we need to move the decimal from the end to in between the 7 and the 6, which is 10 places, hence will be 7.632 times 10 to the power of 10 total mass = 42 + 12 + 6 = 60kg find the total weight by adding water, protein and bone
•  A liquid fertilizer is diluted at a rate of 15ml per 10 litres of water. The label claims that 5L of diluted mixture is required per every 10 square metres of lawn. How many ml of fertilizer is needed to fertilize a 120m2 lawn? 120 ÷ 10 = 12 first we find out how many 10 metres squared are in 120 metres squared by dividing total amount of litres of mixture = 12 × 5 = 60 Litres so we need 12 lots of 5 Litres which is 60 Litres of mixture 60 ÷ 10 = 6 each 10 litres of mixture has 15mls of fertilizer in, so we find out how many lots of 10L is in 60L by dividing 6 × 15 = 90ml we need 6 lots of the fertilizer : which is 6 lots of 15ml
• Water flows from an irrigation pipe at the rate of 2.4m3 every minute. How long would it take for 100 litres of water to flow from the pipe? (1000L = 1m3)?

2.4 × 1000
= 2400L           convert 2.4m3 into litres by multiplying by 1000
2400L              per minute flows through this pipe
100 ÷ 2400
= 0.0416 minutes               to find how long it takes for 100L to flow, divide by 2400 as this gives us 0.0416 minutes 0.0416 × 60
= 2.5 secs                              convert to seconds by multiplying by 60
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• A drop of water contains about 1.7 × 1021 molecules. A typical waterfall may have a flow of 7.5 × 1011 drops of water per minute. How many molecules of water flow over the waterfall in one minute?

1.7 × 1021 × 7.5 × 1011
= 1.275 × 1033

• A bilge pump on a yacht pumps water at the rate of 10ml per second. How long will it take the pump to empty 12 litres of water?

12L = 12000 ml
if it does 10 per second
12000 ÷ 10 = 1200 seconds
1200 ÷ 60 = 20 minutes

•  A tap runs at 9L of water per minute. If you leave the tap on while brushing your teeth for 4.5 minutes each day, how much water would be used in a week brushing your teeth? = 4.5 × 7 = 31.5 minutes per week there are 7 days in a week, so find out the total amount of minutes in the week that the water is used total water = 31.5 × 9 = 283.5L each minute uses 9L, so multiply the 9L by 31.5 minute
•  The average NSW annual water consumption from the residential sector is equal to 90 340 litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%. A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark. How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied? 90 340 × 50 =4 517 000 L each person uses 90 340L a year and there will be 50 people , multiply to find the number of litres for all the people 4 517 000 × 25% = 1 129 250L find 25% of the total amount of litres 1 129 250 ÷ 1000 = 1129.25 KL convert to kilolitres by dividing by 1000 as 1KL = 1000L = 1129KL round to nearest KL