Question

The price of jeans was reduced $\$ 6$ week price for $7$ weeks. By how much did the price of the genes change over the $7$ weeks?

Answer 1

Hint: We have been given the weekly price reduction of the jeans. The price is being reduced regularly for $7$ weeks. We have to find the total reduction in price after $7$ weeks. We can find the total reduction by finding the cumulative reduction over the $7$ weeks.

Complete step by step solution:
We have seen that the price of the jeans is being reduced $\$ 6$ per week. This reduction in price is being done regularly for $7$ weeks.
We have to find the total reduction in the price of the jeans after $7$ weeks.
Let us assume that the original price of the jeans was $\$ x$.
Thus, after $1$ week the price of the jeans gets reduced to
$\$ x - \$ 6 = \$ \left( {x - 6} \right)$
Similarly, after $2$ weeks the price of the jeans gets reduced to
$\$ \left( {x - 6} \right) - \$ 6 = \$ \left( {x - 6 - 6} \right) = \$ \left( {x - 12} \right)$
If we continue this step to calculate the price after each week, after $7$ weeks we will get the price of the jeans as $\$ \left( {x - 42} \right)$.
The total reduction in the price can be calculated as,
$\$ x - \$ \left( {x - 42} \right) = \$ 42$
Hence, the price change of the jeans after $7$ weeks is a total reduction of $\$ 42$.
Alternate Method:
We have been given that the price of the jeans is reduced by $\$ 6$ per week.
Total reduction after $7$ weeks can be calculated as,
\[\$ 6 + \$ 6 + \$ 6 + \$ 6 + \$ 6 + \$ 6 + \$ 6 = \$ 6 \times 7 = \$ 42\]
So, the correct answer is “42”.

Note: The price is being reduced continuously for $7$ weeks, so to find the total reduction we added the reduction per week $7$ times. To find the reduction in the price we did not require the value of the original price or the reduced price. We have to be careful in calculation even as the solution involves simple arithmetic calculations.