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QuestionSipho can choose between two wage options for car washing. Calculate and compare earnings for 12 cars washed.

Studdy Solution

STEP 1

Assumptions1.ipho has two wage options Option1 Wage = R20 per car washed Option Wage = R200 per day + R10 per car washed. n represents the number of cars washed

STEP 2

For Option1, the wageipho earns is directly proportional to the number of cars he washes. The equation representing this isWage=R20×nWage = R20 \times n

STEP 3

For Option2, the wageipho earns is a fixed amount (R200) plus an additional amount that depends on the number of cars he washes. The equation representing this isWage=R200+R10×nWage = R200 + R10 \times n

STEP 4

The break-even point in this context is the number of carsipho needs to wash such that the wage he earns from both options is the same. This can be found by setting the two equations equal to each other and solving for n.
R20×n=R200+R10×nR20 \times n = R200 + R10 \times n

STEP 5

Subtract R10n from both sides to isolate terms with n on one side.
R20×n−R10×n=R200R20 \times n - R10 \times n = R200

STEP 6

implify the left side of the equation.
R10×n=R200R10 \times n = R200

STEP 7

olve for n by dividing both sides by R10.
n=R200/R10n = R200 / R10

STEP 8

Calculate the break-even point.
n=R200/R10=20n = R200 / R10 =20So, the break-even point is whenipho washes20 cars.

STEP 9

Now, let's verify that ifipho had chosen Option and washed12 cars, he would have earned R80 less for the day. First, calculate the wage for Option2 (whichipho chose) when n =12.
WageOption2=R200+R×12Wage_{Option2} = R200 + R \times12

STEP 10

Calculate the wage for Option2.
WageOption2=R200+R10×12=R320Wage_{Option2} = R200 + R10 \times12 = R320

STEP 11

Next, calculate the wage for Option when n =.
WageOption=R20×Wage_{Option} = R20 \times

STEP 12

Calculate the wage for Option.
WageOption=R20×12=R240Wage_{Option} = R20 \times12 = R240

STEP 13

Finally, subtract the wage for Option from the wage for Option2 to find the difference.
Difference=WageOption2−WageOptionDifference = Wage_{Option2} - Wage_{Option}

STEP 14

Calculate the difference.
Difference=R320−R240=R80Difference = R320 - R240 = R80So, ifipho had chosen Option, he would have earned R80 less for the day.

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