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 rectangleLet 3x + 1 = the length of the rectangle

X

3X + 1

X

3X + 1

Let x = the width of the rectangleLet 3x + 1 = the length of the rectangle

34/2 = 3x + 1 + x17 = 4x + 1-1 -116 = 4x÷4 ÷44 = xLength 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) = 5.850.25x + 3.00 - 0.10x = 5.850.15x + 3.00 = 5.85- 3.00 -3.000.15x = 2.85÷0.15 ÷0.15x = 19

Combine x values

Multiply 0.10 into the brackets

Get term with x by itself

Isolate x

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) = 5.850.25x + 3.00 - 0.10x = 5.850.15x + 3.00 = 5.85- 3.00 -3.000.15x = 2.85÷0.15 ÷0.15x = 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. 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. 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 ratioLet 1-x = the amount of cashews in the ratio

2.80x + 3.60(1-x) = 3.122.80x + 3.60 – 3.60x = 3.123.60 – 0.80x = 3.12-3.60 -3.60-0.80x = -0.48÷-0.80 ÷-0.80X = 0.61- x = 0.4

75

75 kilograms of cashews are needed to create this mixture.

Time, Rate and Distance

2h x 100km/h = 200 km

What is the rate if you travel 150 km in 3 h?

How long does it take to travel 900 km at 75 km/h?

900 ÷ 75 = 12

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.

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 ALet 300 + a = the speed of Plane B

3.5a =2.5(300+a)3.5a = 750 + 2.5a-2.5a -2.5aa = 750300+ a = 300 +750 =1050

Before you can answer this

question you must ask your

self what will be equal at the end

That means Plane A is

travelling at 750km/h and

Plane B is travelling at 1050

km/h.Its Distance,

which is calculated by multiplying

speed with time

THAT’S IT FOR NOW