When a bakery opened this morning, the ratio of pineapple muffins to mango muffins was 3:2. After 144 pineapple muffins were sold, the ratio changed to 3:5. How many pineapple muffins were there when the bakery opened in the morning?

So, when the bakery opened this morning, there were 240 pineapple muffins.
Let's denote the initial number of pineapple muffins as 3x and the initial number of mango muffins as 2x, where x is a positive constant.
The initial ratio is given as 3:2, so the total number of muffins when the bakery opened is 3x + 2x = 5x.
After 144 pineapple muffins were sold, the new number of pineapple muffins is 3x - 144, and the new ratio is 3:5.
Now, set up an equation based on the new ratio:
2 x 3 x − 144 ​ = 5 3 ​
Cross-multiply to solve for x :
5 ( 3 x − 144 ) = 3 ( 2 x )
15 x − 720 = 6 x
9 x = 720
x = 80
Now that we know x , we can find the initial number of pineapple muffins:
Initial number of pineapple muffins = 3x = 3 * 80 = 240

Answered by susmthaIRA | 2024-06-24

When the bakery opened, there were 240 pineapple muffins. This was calculated using the initial ratio of pineapple to mango muffins and the revised ratio after selling some muffins. Utilizing algebra, we established the number of muffins based on the given ratios and confirmed the initial count of pineapple muffins.
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Answered by susmthaIRA | 2024-10-11