Question

3.1.3 How far was the hiker at 10:30?

8km
ACTIVITIES
1. Siyabonga runs a car wash business. The monthly expenses for his business include:
R1 400,00 in salaries.
R5,20 per washed car, for water, soap and electricity.
Siyabonga charges R25,00 per car for a wash and vacuum.
1.1.White down a formula to represent the total monthly cost that Siyabonga incurs in running his car
wash business as dependent on the number of cars washed.
(2)
1.2.Write down a formula to represent the total monthly income that Siyabonga generates as dependent
on the number of cars washed.
(2)
1.3. Use trial and improvement to determine how many cars Siyabonga must wash per month in order to
break even and cover all business expenses.(2)
1.4.How much must Siyabonga earn in income per month in order to break even? (2)
1.5.The graphs below resent the total monthly cost and total income for Siyabonga's car wash business.
2.500
2,400
2,300
2 200
2,100
2,000​

Answer 1

`y = 1400 + 5.2x` --- Running cost

`y = 25 x` --- Monthly income

71 cars

R1775

Explanation:

Given

Expenses

`Salaries = 1400.00`

`Others = 5.20` per car

Income

`Rate = 25.00` per car

Solving (a): Expression for the running cost

This is calculated as:

`y = Salary + Others * x`

Where

y = Total running cost

x = number of cars

So:

`y = 1400 + 5.20 * x`

`y = 1400 + 5.2x`

Solving (b): Expression for monthly income

This is calculated as:

`y = Rate * x`

Where

y = Total income

x = number of cars

So:

`y = 25.00 * x`

`y = 25 x`

Solving (c): Break even

To do this, we equate the expressions in (a) and (b)

`y = y`

`25x = 1400 + 5.2x`

Collect Like Terms

`25x -5.2x= 1400`

`19.8x= 1400`

Solve for x

`x = (1400)/(19.8)`

`x = 71`

Solving (d): How much to break even

Substitute 71 for x in any of (a) or (b)

`y = 25 x`

`y = 25 * 71`

`y = 1775`

Solving (e): There is no question to answer on the "graph"