QuestionFind the cost of a plasma TV sold for \$R 17500 with a 70\% markup on cost.

Studdy Solution

STEP 1

Assumptions1. The retail price of the plasma TV is $R17500. The markup percentage based on cost is70%
3. The markup is calculated as a percentage of the cost price4. The retail price includes both the cost price and the markup

STEP 2

First, we need to find the markup amount. We can do this by subtracting the cost price from the retail price.
$Markup\, amount = Retail\, price - Cost\, price$

STEP 3

Since we don't have the cost price, we can express it in terms of the markup amount. From the problem, we know that the markup is70% of the cost price. So we can write $Markup\, amount =70\% \times Cost\, price$

STEP 4

Convert the percentage to a decimal value.
$70\% =0.7$ $Markup\, amount =0.7 \times Cost\, price$

STEP 5

Now, we can substitute the markup amount from2 into the equation from4 to get an equation for the cost price.
$Retail\, price - Cost\, price =0.7 \times Cost\, price$

STEP 6

Rearrange the equation to solve for the cost price.
$Cost\, price = \frac{Retail\, price}{1 +0.}$

STEP 7

Plug in the given value for the retail price to calculate the cost price.
$Cost\, price = \frac{R17500}{1 +0.7}$

STEP 8

Calculate the cost price.
$Cost\, price = \frac{R17500}{1.7} = R10294.12$ The cost of the plasma TV is approximately R10294.12.

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