Question

A certain shade of green is made from six parts yellow mixed with four parts blue. If seventy cans of paint was used in all, how many cans of blue were used?

Answer 1

Hint:
 Assume ‘x’ as the number of yellow cans of paint used and ‘y’ as the number of blue cans of paint used. Now, find the ratio of these colours used and add 1 to both sides of the expression. Substitute the value of (x + y) equal to 70 and find the value of ‘y’ by cross – multiplication to get the answer.

Complete step by step answer:
Here, we have been provided with the information that we are performing a particular shade of green paint which requires six parts of yellow colours cans and four parts of blue colour cans. We have been provided with a total of 70 cans of paint and we are asked to determine the number of blue cans used.
Now, let us assume the number of yellow cans and blue cans of paint used are ‘x’ and ‘y’ respectively. Since, to form the shade of green, we are using six yellow parts and four blue parts. So, the required ratio in which these colours are mixed will be given as: -
\[\Rightarrow \dfrac{x}{y}=\dfrac{6}{4}\]
Cancelling the common factors, we get,
\[\Rightarrow \dfrac{x}{y}=\dfrac{3}{2}\]
Adding 1 both sides we get,
\[\begin{align}
  & \Rightarrow \dfrac{x}{y}+1=\dfrac{3}{2}+1 \\
 & \Rightarrow \dfrac{x+y}{y}=\dfrac{3+2}{2} \\
 & \Rightarrow \dfrac{x+y}{y}=\dfrac{5}{2} \\
\end{align}\]
Clearly, we can see that in the above expression, (x + y) denotes the sum of the number of yellow paints and the number of blue paints used. It is given in the question that a total of 70 cans of paint was used, therefore the sum of x and y will be 70. So, we have,
\[\Rightarrow \dfrac{70}{y}=\dfrac{5}{2}\]
By cross – multiplication we get,
\[\begin{align}
  & \Rightarrow y=\dfrac{70\times 2}{2} \\
 & \Rightarrow y=28 \\
\end{align}\]
Hence, the number of blue cans used is 28.

Note:
 One may note that there are several small methods to solve the question. The other method can be started with determining the number of cans of green paint that will be formed by the addition of colours. We can see that 1 can of green paint will be formed by a total of 10 cans of both the colours provided. Now, find the total number of cans of green that can be formed by 70 cans of the two paints. Now, consider that if 1 can of green is formed by 4 cans of blue then how many cans of blue will be required to form 7 cans of green. Determine the answer by using the unitary method.