Basket candy ratio

There are lollipops, chocolates, and candies in the basket. The number of lollipops and chocolates is in the ratio of 2:3, and the number of chocolates and candies is in the ratio of 4:5. There are 15 fewer candies than lollipops and chocolates combined. How many candies are there in the basket?

Final Answer:

n =  105

Step-by-step explanation:

$$\begin{gathered} a:b=2:3 \\ b:c=4:5 \\ c=a+b-15 \\ n=a+b+c \\ 3a=2b \\ 5b=4c \\ c=a+b-15 \\ c=2/3\cdot b+b-15 \\ c=(1+2/3)\cdot b-15 \\ c=(1+2/3)\cdot \frac{4}{5}\cdot c-15 \\ c=(1+2/3)\cdot 4/5\cdot c-15 \\ 5c=225 \\ c=\frac{225}{5}=45 \\ c=45 \\ b=\frac{4}{5}\cdot c=\frac{4}{5}\cdot 45=\frac{4\cdot 45}{5}=\frac{180}{5}=36 \\ a=\frac{2}{3}\cdot b=\frac{2}{3}\cdot 36=\frac{2\cdot 36}{3}=\frac{72}{3}=24 \\ n=a+b+c=24+36+45=105 \end{gathered}$$

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