8.4 Word Problems Math 9

The length of a rectangular garden is 1 m more than three times the garden’s width. If the perimeter of the garden is 34 m, find its dimensions.

The length of a rectangular garden is 1 m more than three times the garden’s width. If the perimeter of the garden is 34 m, find its dimensions. Let x = the width of the rectangle Let 3x + 1 = the length of the rectangle 3X + 1 X X 3X + 1

Let x = the width of the rectangle Let 3x + 1 = the length of the rectangle 34/2 = 3x + 1 + x 17 = 4x + 1 -1 -1 16 = 4x ÷4 ÷4 4 = x Length of rectangle: 3x + 1 = 3(4) + 1 = 13 The width of the rectangle is 4 and the length of the rectangle is 13. X 3X + 1

The cash register in the school canteen contains x quarters and (30 – x) dimes. If the total value of the coins is $5.85, how many of each kind of coin are there?

The cash register in the school canteen contains x quarters and (30 – x) dimes. If the total value of the coins is $5.85, how many of each kind of coin are there? 0.25x + 0.10(30-x) = 5.85 0.25x + 3.00 - 0.10x = 5.85 0.15x + 3.00 = 5.85 - 3.00 -3.00 0.15x = 2.85 ÷0.15 ÷0.15 x = 19 Multiply 0.10 into the brackets Combine x values Get term with x by itself Isolate x

There are 11 dimes and 19 quarters in the canteen The cash register in the school canteen contains x quarters and (30 – x) dimes. If the total value of the coins is $5.85, how many of each kind of coin are there? 0.25x + 0.10(30-x) = 5.85 0.25x + 3.00 - 0.10x = 5.85 0.15x + 3.00 = 5.85 - 3.00 -3.00 0.15x = 2.85 ÷0.15 ÷0.15 x = 19 Dimes = 30 – x = 30 – 19 = 11 There are 11 dimes and 19 quarters in the canteen

An employee mixes peanuts worth $2. 80/kg with cashews worth $3. 60/kg An employee mixes peanuts worth $2.80/kg with cashews worth $3.60/kg. She sells the mixture for $3.12/kg. If she has 75 kg of peanuts, how many kilograms of cashews does she need?

An employee mixes peanuts worth $2. 80/kg with cashews worth $3. 60/kg An employee mixes peanuts worth $2.80/kg with cashews worth $3.60/kg. She sells the mixture for $3.12/kg. If she has 75 kg of peanuts, how many kilograms of cashews does she need? Let x = the amount of peanuts in the ratio Let 1-x = the amount of cashews in the ratio 2.80x + 3.60(1-x) = 3.12 2.80x + 3.60 – 3.60x = 3.12 3.60 – 0.80x = 3.12 -3.60 -3.60 -0.80x = -0.48 ÷-0.80 ÷-0.80 X = 0.6 1- x = 0.4 0.4 0.6 = 𝑥 75 75∗0.4÷0.6=50 75 kilograms of cashews are needed to create this mixture.

Time, Rate and Distance 2h x 100km/h = 200 km 2ℎ 1 ∗ 100 𝑘𝑚 1ℎ =200𝑘𝑚 How long does it take to travel 900 km at 75 km/h? 900 ÷ 75 = 12 900 𝑘𝑚 1 ∗ 1 ℎ 75 𝑘𝑚 =12 What is the rate if you travel 150 km in 3 h? 150 𝑘𝑚 3 ℎ = 50 𝑘𝑚 1 ℎ 𝑜𝑟 50 𝑘𝑚/ℎ

Plane A leaves the airport Plane A leaves the airport. One hour later, Plane B leaves the same airport on the same course. It catches up to Plane A in 2 ½ h. The average speed of Plane B is 300 km/h faster than Plane A. Find the speed of each plane.

Its Distance, which is calculated by multiplying speed with time Plane A leaves the airport. One hour later, Plane B leaves the same airport on the same course. It catches up to Plane A in 2 ½ h. The average speed of Plane B is 300 km/h faster than Plane A. Find the speed of each plane. Let a = the speed of Plane A Let 300 + a = the speed of Plane B 3.5a =2.5(300+a) 3.5a = 750 + 2.5a -2.5a -2.5a a = 750 300+ a = 300 +750 =1050 That means Plane A is travelling at 750km/h and Plane B is travelling at 1050 km/h. Before you can answer this question you must ask your self what will be equal at the end Its Distance, which is calculated by multiplying speed with time

That’s it for now