Question

Weiming, Joyce and Siti divide cookies to sell in a ratio of 5: 12: 9. After Weiming sold 28 cookies, the ratio becomes 1: 8: 6. How many cookies did they have in the first place?

Answer 1

216 cookies

Explanation:

From the question,

Let the total cookies in the first place be x cookies.

Their ratio = 5:12:9

Total = 5+12+9 = 26.

Weiming share = (5/26)x = 5x/26

If weiming sold 28 cookies

⇒ (5x/26)-28

⇒ (5x-728)/28

Hence Weiming new share = (5x-728)/28 cookies

The new ratio is 1:8:6

The total cookies becomes = x-28

Therefore,

(1/15)(x-28) = (5x-728)/28

(x-28)/15 = (5x-728)/28

Crossmultiply

28(x-28) = 15(5x-728)

28x-784 = 75x-10920

Collect like terms

28x-75x = -10920+784

-47x = -10136

x = -10136/-47

x = 215.7

x ≈ 216 cookies