Chapter 3.6, Problem 6P

To determine

To find:thenumber of each type of bin are there if the capacity of the warehouse is 510 tons.

Answer to Problem 6P

The number of the big bins and small bins are 18 and 12, respectively.

Explanation of Solution

Given information:

A grain-storage warehouse has a total of 30 bins.

Big bin hold 20 tons of grain for each and small bin hold 15 tons of the grain for each.

Calculation:

Let xbe the number of the big bins and y be the number of the small bins.

Since the total number of the bins is 30, it can be written as the equation $x+y=30$ .

The capacity of the warehouse is 510 tons, so it can be written as the equation $20x+15y=510$ .

Compute the solutions of the system $x+y=30$ and $20x+15y=510$ by linear combination method.

Multiply the equation $x+y=30$ by 20. That is, $20x+20y=600$ .

Subtract the equation $20x+15y=510$ from the equation $20x+20y=600$ .

  $\begin{array}{l}20x+20y=600\\ 20x+15y=510\\ \overline{0x+5y=90}\end{array}$

Divide on both sides by5,

  $\begin{array}{l}\frac{5y}{5}=\frac{90}{5}\\ y=18\end{array}$

Substitute $y=18$ in $x+y=30$ and simplify the value of x ,

  $\begin{array}{l}x+18=30\\ x=30-18\\ x=12\end{array}$

Therefore, the number of the big bins and small bins are 18 and 12, respectively.