A baker bakes a batch of muffins and splits the batch evenly onto six different trays. She then adds five croissants to each tray. If each tray now contains at least twenty baked goods, what is the least possible number of muffins in the baker's original batch?
I don't even know where to start, if you could help me, I would really appreciate it.
If each tray originally had n muffins
n + 5 >= 20
n >= 15
so, there were originally 6n >= 90 muffins
m= muffins in original batch
So, each tray has m/6 muffins and 5 croissants, which totals m/6+5. The value must be at least 20, so we have this inequality:
m/6+5 is greater than or equal to 20. We multiple each side by 6 and get:
m is greater than or equal to 90 muffins.
ANSWER: Original batch had 90 muffins
To find the least possible number of muffins in the baker's original batch, we first need to consider the number of trays and the total number of baked goods.
Let's assume the number of muffins in the original batch is "M". The baker splits the batch evenly onto six different trays, so each tray will have M/6 muffins.
The baker then adds five croissants to each tray, resulting in a total of M/6 + 5 baked goods on each tray.
Since each tray must have at least twenty baked goods, we can set up the following inequality:
M/6 + 5 ≥ 20
To find the least possible value of M, we need to solve this inequality.
First, subtract 5 from both sides of the inequality:
M/6 ≥ 15
Next, multiply both sides of the inequality by 6 to eliminate the denominator:
M ≥ 90
Therefore, the least possible number of muffins in the baker's original batch is 90.