Candy color ratio

There are white, red, and green candies in the package. The number of white and red candies is in the ratio of 1:3, and the number of red and green candies is in the ratio of 4:7. There are 20 more green candies than white and red combined. How many candies are there?

Final Answer:

x =  148

Step-by-step explanation:

$$\begin{gathered} 3b=c \\ 7c=4z \\ z=20+b+c \\ 3\cdot b=c \\ 7\cdot c=4\cdot z \\ 3b-c=0 \\ 7c-4z=0 \\ b+c-z=-20 \\ Row3-\frac{1}{3}\cdot Row1\to Row3 \\ 1.333c-z=-20 \\ Row3-\frac{1.33333333}{7}\cdot Row2\to Row3 \\ -0.238z=-20 \\ z=\frac{-20}{-0.23809524}=84 \\ c=\frac{0+4z}{7}=\frac{0+4\cdot 84}{7}=48 \\ b=\frac{0+c}{3}=\frac{0+48}{3}=16 \\ b=16 \\ c=48 \\ z=84 \\ x=b+c+z=16+48+84=148 \end{gathered}$$

Try another example