In a bakery, the ratio of the number of muffins to the number of donuts was 8:5. If 1/4 of the muffins were sold, what faction of the donuts must be sold so that the ratio of the number of muffins to the number of donuts left is 2:1?
muffins : donuts = 8:5 = 8x : 5x
1/4 of muffins sold, so now we only have 6x
new amount of donuts needed so that 6x : kx = 2:1
2kx = 6x
k = 3
so we will need 3x of donuts
but we had 5x, so k(5x) = 3x
k = 3/5
we have to sell 2/5 of the donuts
check:
suppose we had 160 muffins and 100 donuts
we sold 1/4 of the muffins, so we have 120 muffins left
we also sell 2/5 of the 100 donuts, leaving us with 60
and 120 : 60 = 2:1