Question

If recyclers pay $\$5$ a ton for newspapers, how many tons of newspaper would your school have to recycle to earn \[\$75\]?

Answer 1

Hint: In order to find a solution to this problem, we will have to first convert this word problem into mathematical format and then after converting into mathematical form, we will have to create an equation. After creating an equation, we will solve the problem and then verify it.

Complete step-by-step solution:
As we know, we have our problem as a word problem, so we will first convert it into a mathematical problem.
Therefore, breaking down our problem into parts, we get:
Recycler price for one ton $\$5$
Total price school wants $\$75$
Let how many tons of newspaper would the school have to recycle to earn \[\$75\] be $x$.
Hence, that can be written as $5x$
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:
$\Rightarrow 75=5x$
Now on dividing both side by $5$ , we get our equation as:
$\Rightarrow \dfrac{75}{5}=\dfrac{5x}{5}$
On simplifying, we get our solution as:
$\Rightarrow x=15$
Therefore, it requires the school to recycle $15$ tons of newspaper to earn $\$75$.

Note: Since it is a pre-algebraic problem we must have to have a deep understanding in pre-algebra.
Pre-algebra is the mathematical skills required to perform the basic operations assumed in algebraic manipulations.
Now, 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 to see if our answer is correct or not.
We have our equation as:
$\Rightarrow 75=5x$
Now, we will substitute $x=15$ in our above equation and see if it is equal to the left-hand side of our equation.
On substituting, we get:
$\Rightarrow 5\left( 15 \right)$
On simplifying, we get:
$\Rightarrow 75$
That’s equal to the left-hand side.
$\Rightarrow 75=75$
Therefore, we can say that our solution is correct.