The cost of purchasing 3 organic oranges and 5 organic apples at a store
is $45. If one organic apple costs $3.75 more than one of the oranges,
what is the total cost of 10 of the same apples and 10 of the same
oranges?
Let's start by finding the cost of one organic orange. Let's assume the cost of one organic orange is x.
Therefore, the cost of one organic apple would be x + $3.75.
The cost of 3 organic oranges would be 3x.
The cost of 5 organic apples would be 5(x + $3.75).
According to the problem, 3x + 5(x + $3.75) = $45.
Simplifying the equation gives 3x + 5x + $18.75 = $45.
Combining like terms gives 8x + $18.75 = $45.
Subtracting $18.75 from both sides gives 8x = $45 - $18.75.
Simplifying the equation gives 8x = $26.25.
Dividing both sides of the equation by 8 gives x = $26.25 / 8 = $3.28125.
Therefore, the cost of one organic orange is $3.28125 and the cost of one organic apple is $3.28125 + $3.75 = $7.03125.
The total cost of 10 organic oranges would be 10 * $3.28125 = $32.8125.
The total cost of 10 organic apples would be 10 * $7.03125 = $70.3125.
Therefore, the total cost of 10 organic apples and 10 organic oranges would be $32.8125 + $70.3125 = $103.125. Answer: \boxed{103.125}.