ExplanationThe equation for the situation described is 7x + 6y = 95, where x stands for the number of batches of chocolate chip cookies and y stands for the number of batches of peanut butter cookies.
It looks as though this equation is not solvable, because there are two variables and only one equation. However, since the baker can only make whole batches, x and y must be integers, which really limits the possibilities.
Furthermore, the question asks for the minimum number of chocolate chip cookies the baker could have made. So, try 1 for x and see if you get an integer for y (use your calculator when needed!):
\(7(1) + 6y = 95\)
\(6y = 88\)
\(y = 14.6\)…
Since this did not result in an integer number of batches of peanut butter cookies, this situation doesn’t work. Try 2, 3, 4, etc. for x. (Don’t try values out of order—remember, there might be more than one x value that works, but you need to be sure that you have the smallest one!)
The smallest value that works for x is 5:
\(7(5) + 6y = 95\)
\(6y = 60\)
\(y = 10\)
Remember that you need the minimum number of chocolate chip cookies, not batches of cookies.
Since the minimum number of batches is 5 and there are 7 cookies per batch, the minimum number of chocolate chip cookies is 35.
Hence option E is correct!
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