# Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

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{\text{A}}{\text{. 16}} \\

{\text{B}}{\text{. 17}}{\text{.5}} \\

{\text{C}}{\text{. 20}}{\text{.5}} \\

{\text{D}}{\text{. 24}} \\

{\text{E}}{\text{. 35}} \\

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Last updated date: 18th Mar 2023

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Answer

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Hint- Here, we will be proceeding by firstly finding out the sales for the second year of the business with the help of the given relationship between the sales for the second year and the third year and then in the similar fashion, obtaining the sales for the first year of the business (in million dollars).

Given, sales for the third year = 38 million dollars

Also, given that sales for the third year were double the sales for the second year

i.e., sales for the third year = 2(sales for the second year)

$ \Rightarrow $ sales for the second year$ = \dfrac{{{\text{sales for the third year}}}}{2} = \dfrac{{38}}{2} = 19$ million dollars

Also, given that the sales for the business were 3 million dollars more the second year than the first year which means that the difference between the sales for the first year and the second year is 3 million dollars where sales for the second year is more than the sales for the first year.

i.e., sales for the second year = sales for the first year +3

$ \Rightarrow $ sales for the first year = sales for the second year -3 = 19-3 = 16 million years

Therefore, the sales for the first year is 16 million years.

Hence, option A is correct.

Note- In these types of problems, correct formulation of the problem statement into the equations is done. According to the problem statement, relation between the sales for the first and second years and relation between the sales for the second and third years are obtained and we already have the value of the sales for the third year. From there, sales for the first year can be determined easily.

Given, sales for the third year = 38 million dollars

Also, given that sales for the third year were double the sales for the second year

i.e., sales for the third year = 2(sales for the second year)

$ \Rightarrow $ sales for the second year$ = \dfrac{{{\text{sales for the third year}}}}{2} = \dfrac{{38}}{2} = 19$ million dollars

Also, given that the sales for the business were 3 million dollars more the second year than the first year which means that the difference between the sales for the first year and the second year is 3 million dollars where sales for the second year is more than the sales for the first year.

i.e., sales for the second year = sales for the first year +3

$ \Rightarrow $ sales for the first year = sales for the second year -3 = 19-3 = 16 million years

Therefore, the sales for the first year is 16 million years.

Hence, option A is correct.

Note- In these types of problems, correct formulation of the problem statement into the equations is done. According to the problem statement, relation between the sales for the first and second years and relation between the sales for the second and third years are obtained and we already have the value of the sales for the third year. From there, sales for the first year can be determined easily.

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