Question

A firm has two grades of coffee beans, Grade A and Grade B. 40 kg of Grade A and 45 kg of Grade B are to be mixed and packaged into two types of packets of 1 kg each — economy type and special type. The economy pack consists of beans of Grade A and Grade B in the ratio 1 : 3. The special pack consists of beans of Grade A and Grade B in equal proportion. Find the number of economy and special packs that can be made, using the substitution method.

Answer 1

Answer on Question #67099 – Math – Algebra

Question

A firm has two grades of coffee beans, Grade A and Grade B. 40 kg of Grade A and 45 kg of Grade B are to be mixed and packaged into two types of packets of 1 kg each — economy type and special type. The economy pack consists of beans of Grade A and Grade B in the ratio 1 : 3. The special pack consists of beans of Grade A and Grade B in equal proportion. Find the number of economy and special packs that can be made, using the substitution method.

Solution

We denote the number of economy packs by $x$, and the number of special packs by $y$. In 1 kg of an economy pack there will be 0.25 kg of Grade A and 0.75 kg of Grade B. In 1 kg of a special pack there will be 0.5 kg of Grade A and 0.5 kg of Grade B.

Let us compose a system of linear equations for this task:

$$\left\{ \begin{array}{l} 0.25x + 0.5y = 40 \\ 0.75x + 0.5y = 45 \end{array} \right.$$

Now we solve this equation by the substitution method.

It follows from the first equation of the system that

$$0.25x + 0.5y = 40$$ $$0.25x = 40 - 0.5y$$ $$x = 160 - 2y$$

Substituting for $x$ into the second equation of the system

$$0.75(160 - 2y) + 0.5y = 45$$ $$120 - 1.5y + 0.5y = 45$$ $$y = 75$$ $$x = 160 - 2 \cdot 75$$ $$x = 10$$

Thus, from a given number of grains you can make 10 economy packs and 75 special packs.

Answer:

10 economy packs and 75 special packs.

Answer provided by https://www.AssignmentExpert.com