Applicaons of Percent

Applications of Percent A rao is a comparison of quantities measured in the same units. A rate is a comparison of quantities measured in different units. E.g. Fuel consumption of a car 5.7 L/100 km A statement that two raos are equal is called a proporon. E.g. a:b=c:d or . 𝑎𝑏 = 𝑐 𝑑 a to b=c to d Example 1 : Solve the following proporons. a) 38 = 𝑚 24 LCD(8,24)=24 24 38 ( ) = 24 𝑚 24 ( ) 3 3 ( ) = 𝑚 9 = 𝑚 OR cross multiply 38 = 𝑚 24 8𝑚 = 3 ×24 8𝑚 = 72 8𝑚 8 = 72 8

𝑚 = 9 b) 5 13 = 10 𝑦 5𝑦 = 10 ×13 5𝑦 = 130 5𝑦 5 = 130 5 𝑦 = 26 OR 13 5 = 𝑦 10 So, LCD(5,10)=10 10 13 5 ( ) = 10 𝑦 10 ( ) 2 13 ( ) = 𝑦 26 = 𝑦 OR 5 13 = 10 𝑦 5 ×2 13 ×2 = 10 𝑦 1026 = 10 𝑦

So, y=26 Example 2 : A car's fuel consumpon is quoted as 8.5 L/100 km. a) Find how much fuel is needed to travel 350 km. b) Find how far the car will travel on 58 L of gasoline. Solution: a) Let x represent the amount of fuel needed to travel 350 km. 8.5 100 = 𝑥 350 350 8.5 100 ( ) = 350 𝑥 350 ( ) 350 ×8.5 100 = 𝑥 𝑥 = 2975 100 𝑥 = 29. 75 29.75 L of fuel is needed to travel 350 km. b) Let t represent the distance the car can travel on 58 L of gas. 8.5 100 = 58 𝑥 8. 5𝑥 = 58 ×100 8. 5𝑥 = 5800 8.5𝑥 8.5 = 5800 8.5 𝑥 = 682. 4 You can travel approx.. 682.4 km on 58 L of gasoline.

Example 3 : John works part-time at a clothing store. He earns $80 per week plus 7% of the value of his weekly sales. This week John earns $121.What is the total value of his sales this week? Solution: Let y rep. the value of John`s weekly sales. 80+7% of y =121 80 + 0. 07𝑦 = 121 0. 07𝑦 = 121 − 80 0. 07𝑦 = 41 0.07𝑦 0.07 = 41 0.07 Total value of his sales for this week is $585.71 Example 5 : On a map, two towns are 85 mm apart. If the scale of the map is 1:1500000, what is the actual distance between the towns. Solution: 1mm on the map represent 1500000 mm of the actual distance. Let x rep. the actual distance between the two towns. 1 1500000 = 85 𝑥 𝑋 = 85 ×1500000 X=127500000 mm 1m=1000 mm 1km=1000 m 1𝑘𝑚 = 1000 ×1000 𝑚𝑚 =1000000 mm

𝑥 = 127500000 1000000 =127.5 km The distance between the two towns is 127.5 km.