Question

On Snigadh’s birthday, her father brought a flower bouquet that contains 18 flowers in all. If the ratio of red flowers to yellow is 1:2. Find their number.

Answer 1

Hint: To solve this question, we will, first of all, assume a variable for the ratio and then calculate the number of flowers that are red and yellow in terms of their ratio. Finally, we will equate their sum to the total number of flowers, i.e. 18 to get the value of x.

Complete step-by-step solution
We are given that the bouquet which Snigadh’s father brought has 18 flowers in it. Therefore, the total number of flowers is 18.
We are given that the ratio of red flowers to that of the yellow flowers is given by 1:2. Let us assume a ratio to calculate the number of flowers. Let the ratio be x. Then as the total number of flowers is equal to the sum of the red flowers and yellow flowers.
Total Flowers = Red Flowers + Yellow Flowers
As the ratio is 1:2, therefore we get,
Red flowers = x and yellow flowers = 2x.
\[\Rightarrow \text{Total Flowers}=x+2x\]
We are given that the total flowers are 18.
\[\Rightarrow x+2x=18\]
\[\Rightarrow 3x=18\]
Now, dividing both the sides by 3, we get,
\[\Rightarrow x=\dfrac{18}{3}\]
\[\Rightarrow x=6\]
So, the value of the ratio is x = 6.
Finally, we will calculate the number of flowers using this obtained value of x. Therefore we get,
\[\text{Number of red flowers}=1x\]
\[\Rightarrow \text{Number of red flowers}=1\times 6\]
\[\Rightarrow \text{Number of red flowers}=6\]
Therefore, we get the number of red flowers as 6.
Now, the number of yellow flowers is 2x.
\[\Rightarrow \text{Number of yellow flowers}=2x\]
\[\Rightarrow \text{Number of yellow flowers}=2\times 6\]
\[\Rightarrow \text{Number of yellow flowers}=12\]
Therefore, the number of yellow flowers is 12.

Note: Because the ratio was 1:2 of red to yellow flowers, 1x to 2x type value and as when x > 0, we have $2x > 1x$. Therefore, the number of yellow flowers will always be greater than the number of red flowers. Here, $x > 0$ as the number of flowers can never be negative in the number. Either it will be 0 or a positive number.