Question

A gardener buys fifty carrot seeds and twenty lettuce seeds for $\$1.10$ and her mother buys thirty carrot seeds and forty lettuce seeds for $\$1.50.$ Find the cost of one carrot seed and one lettuce seed.

Answer 1

Hint: For solving this question you should know about the general equation representation and solving them to find the values of variables from that equation. In this problem first we will make the equations from the given statement data and then we will solve both the equations for getting the required values of both vegetable seeds.

Complete step by step answer:
So, according to our question it is asked to us to find the value of one carrot and one lettuce seed if the total price of both in quantities are given.
So, here first we will see the statements and make the equation from them.
Let us consider that carrot seeds \[=x\]
And Lettuce seeds \[=y\]
According to the question gardener buys fifty carrot seeds and twenty lettuce seeds for $\$1.10$, it can be written as \[50x+20y=1.10\] - (1)
And her mother buys thirty carrot seeds and forty lettuce seeds in $\$1.50$, it can be written as,
\[30x+40y=1.50\] - (2)
From equation (1) – equation (2)
\[\begin{align}
  & 100x+40y=2.20 \\
 & 30x+40y=1.50 \\
 & \underline{--} \\
 & 70x+0=0.70 \\
\end{align}\]
\[x=0.01\]
And put this value of x in equation (1)
\[50\times \left( 0.01 \right)+20y=1.10\]
 \[\begin{align}
  & 20y=1.10-{0.5} \\
 & y=\dfrac{0.6}{20} \\
 & y=0.03 \\
\end{align}\]
So, the value of one carrot seed is $\$0.01$ and one lettuce seed is $\$0.03$.

Note: While solving these types of questions you have to be careful when you form the equation form the statement because if any variable will be disturb from its place or if it leaves by mistake then we can’t do anything because then all the questions will be wrong so care about it.