Answer Key
University
High SchoolCourse
MPM1D | Principles of MathematicsPages
5
Academic year
2023
anon
Views
16
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 . ππ = π π a to b=c to d Example 1 : Solve the following proporons. a) 38 = π 24 LCD(8,24)=24 24 38 ( ) = 24 π 24 ( ) 3 3 ( ) = π 9 = π OR cross multiply 38 = π 24 8π = 3 Γ24 8π = 72 8π 8 = 72 8
π = 9 b) 5 13 = 10 π¦ 5π¦ = 10 Γ13 5π¦ = 130 5π¦ 5 = 130 5 π¦ = 26 OR 13 5 = π¦ 10 So, LCD(5,10)=10 10 13 5 ( ) = 10 π¦ 10 ( ) 2 13 ( ) = π¦ 26 = π¦ OR 5 13 = 10 π¦ 5 Γ2 13 Γ2 = 10 π¦ 1026 = 10 π¦
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 = π₯ 350 350 8.5 100 ( ) = 350 π₯ 350 ( ) 350 Γ8.5 100 = π₯ π₯ = 2975 100 π₯ = 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 π₯ 8. 5π₯ = 58 Γ100 8. 5π₯ = 5800 8.5π₯ 8.5 = 5800 8.5 π₯ = 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. 07π¦ = 121 0. 07π¦ = 121 β 80 0. 07π¦ = 41 0.07π¦ 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 π₯ π = 85 Γ1500000 X=127500000 mm 1m=1000 mm 1km=1000 m 1ππ = 1000 Γ1000 ππ =1000000 mm
π₯ = 127500000 1000000 =127.5 km The distance between the two towns is 127.5 km.
Applicaons of Percent
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