Question

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

Answer 1

so
pinaple:mango=3:2

after 144 pinaple was sold (-144 pinaple)
the ratio changed to 3:5

one way is to convert the second number of both ratios to the same number, since they (mangos) didn't change
3:2=15:10
3:5=6:10

so
15 pinaple units-144=6 pinaple units
add 144 to both sides
15p=6p+144
subtract 6p (pinaple units) from bothsides
9p=144
divide both sides by 9
pinaple unit=16
there were 15 units in the begining so
in the beginning, ther were 15 times 16 pinaples or 240 pinaple muffins


240 is the answer

Answer 2

In the Beginning Ratio of the number of pineapple muffins to mango muffins =3:2

Let the the number of pineapple muffins and mango muffins be 3 k and 2 k.

Number of pineapple muffins sold = 144

New Ratio of the number of pineapple muffins to mango muffins is 3:5.

⇒
`(3k - 144)/(2k)=(3)/(5)`

⇒5 × (3 k - 144) = 2 k × 3

⇒ 15 k - 720 = 6 k [ Using Distributive property: a × (b+ c) = a × b + a × c]

⇒15 k - 6 k = 7 20 [ Taking variable on one side and constant on another side of equation]

⇒9 k = 720

Dividing both sides by 9, we get

k = 80

So, Number of pineapple muffins which were present in the store when the bakery opened = 80 × 3 = 240