Question

How many pounds of corn can you buy if your total spending cash is \[\$11.61\] and tomatoes are selling for \[\$1.29\] per pound and corn is selling for \[\$3.25\] per pound and you buy $6$ pounds of tomatoes?

Answer 1

Hint: In order to find a solution to this problem, we will have to use five steps of solving word problems. These five steps help us to solve word problems easily, they are Identify the Problem, Gather Information, To Create an Equation, Solve the Problem and Verify the Answer. Also, we will use some concepts of linear models in this problem.

Complete step-by-step solution:
As we have a linear model mathematical word problem, we will use the concept of linear model that is to let the variable be whatever the question asks you to find.
For example, Find the number. So, it can be: Let the number be $x$ .
Now, coming to our problem, as we have identified the problem, we will now gather information.
Therefore, breaking down our problem into parts, we get:
Total spending cash: $11.61$
Tomato selling price: $1.29$
Corn selling price: $3.25$
Pounds of tomato we can buy: $6$ that is can be written as $6\times 1.29$
And Let pounds of corn we can buy be $x$.
And pounds of corn we can buy can be written as: $3.25x$
Now, as we have gathered information, we will now create an equation based on the problem.
Therefore, on creating an equation and solving the equation, we get:
\[11.61=\left( 6\times 1.29 \right)+3.25x\]
On simplifying right-hand side, we get:
\[\Rightarrow 11.61=7.74+3.25x\]
On taking similar term on left-hand side, we get our equation as:
\[\Rightarrow 11.61-7.74=3.25x\]
On simplifying, we get:
\[\Rightarrow 3.87=3.25x\]
Now on dividing both side by $3.25$, we get our equation as:
\[\Rightarrow \dfrac{3.87}{3.25}=\dfrac{3.25x}{3.25}\]
On simplifying, we get:
$\Rightarrow x=1.191$
Therefore, we can buy $1.191$ pounds of corn if our total spending cash is \[\$11.61\]

Note: Now, since we are working with a linear model, we will lastly verify if our answer is correct or not.
Therefore, to do this we will equate our answer in our original equation and see if the other side of the number is equal to our other side's answer.
We have our equation as:
\[11.61=6\left( 1.29 \right)+3.25x\]
Now, we will substitute $x=1.191$ in our above equation and see if it is equal to the left-hand side of our equation.
On substituting, we get:
$\Rightarrow \left( 6\times 1.29 \right)+\left( 3.25\times 1.191 \right)$
On simplifying, we get:
$\Rightarrow 7.74+3.87$
On adding, we get:
$\Rightarrow 11.61$
That’s equal to the left-hand side.
$\Rightarrow 11.61=11.61$
Therefore, we can say that our solution is correct.