Equations and inequalities are tools that help us explain and solve problems. Bo

Question

Equations and inequalities are tools that help us explain and solve problems. Both are helpful!

For your initial response:

Complete both parts.

a) Choose one of the following equations or inequalities from the list below and create a scenario to go along with the equation or inequality then solve for your variable. Please show your work.

Here is an example to help you get started!

Equation: 3 + 0.10x = 5

Scenario: I need to purchase a half gallon of milk and the price is $3.00. I also want to purchase apples and the price is $0.10 per apple. If I want to spend exactly $5, how many apples can I buy?

Let x = the number of apples. Solve for x to find the number of apples.
$3 + $0.10x = $5
$3 - $3 + $0.10x = $5 - $3   Subtract $3 from both sides
$0.10x/$0.10 = $2/$0.10   Divide both sides by $0.10
x = 20 apples
I can buy 20 apples.

Choose from one of the equations/inequalities below:

1. 6x + 5 = 23

2. 10y – 18 = 82

3. 0.09x + 7 30

4. 4w + 8 = 24

5. 2y + 3 < 103

6. 8.75x + 15 = 163.75

7. x + .15x = 40.25  

8. y + .2y < 10

9.   12x + 5 < 65

10. 2.75 + 22x = 134.75

b) Create your own linear equation or inequality for your classmates to solve.

Explanation / Answer

Equation: 6x + 5 = 23

Scenario: I have to hire a taxi to reach the Airport. On the way I stopped at a coffee shop which was 1km far from the starting point. The taxi fare is $5 for the first kilometre and $6/km for the subsequent distance. The taxi driver charged $23 for the journey. How far is the airport from the coffee shop?

Let x be distance from the coffee shop to the airport. The fare for the first kilometre (i.e., $5) is the charge to reach the coffee shop.

The fare for x km=6x

Total Fare=5 + 6x,Which is also given as 23

Therefore, 5 + 6x = 23

Subtracting 5 from both sides, 5 + 6x - 5 = 23 - 5

i.e., 6x = 18

Dividing both sides by 6, we get, 6x÷6 = 18 ÷ 6

Therefore, x=3

Hence, the distance between coffee shop and airport is 3km.

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