Chapter 8.10, Problem 22PPS

(a)

To determine

The system of equations which represent the given problem conditions

Answer to Problem 22PPS

The system of equations is:

  $\begin{array}{l}2x+2y=8.80\\ 3x+4y=7.80\end{array}$

Explanation of Solution

Given:

Two conditions given in problem:

Cost of $2$ bagels and $2$ cans of orange juice is $\$4.40$ .

Cost of $3$ bagels and $4$ cans of orange juice is $\$7.80$ .

Consider;

The cost of bagels: $x$

The cost of one can of orange juice: $y$

Now, write the equations for two problem conditions:

  $2x+2y=8.80$....... (1)

  $3x+4y=7.80$....... (2)

Conclusion:

Thus, the equation system is written as:

  $\begin{array}{l}2x+2y=8.80\\ 3x+4y=7.80\end{array}$ .

(b)

To determine

The solutions of system equations which represent the given problem conditions and the meaning of the solutions is to be explained.

Answer to Problem 22PPS

The cost of bagels is $\$1.00$ and the cost of one can of orange juice is $\$3.40$ .

Explanation of Solution

Given:

Two conditions given in problem:

Cost of $2$ bagels and $2$ cans of orange juice is $\$4.40$ .

Cost of $3$ bagels and $4$ cans of orange juice is $\$7.80$ .

Consider;

The cost of bagels: $x$

The cost of one can of orange juice: $y$

Now, write the equations for two problem conditions:

  $2x+2y=8.80$....... (1)

  $3x+4y=7.80$....... (2) Now, multiple by $2$ to eq. (1):

  $4x+4y=1.00$....... (3)

Now take subtraction of eq. (2) and (3):

  $\begin{array}{l}4x+4\cancel{y}=17.60\\ 3x+4\cancel{y}=7.80\\ ---\\ ----------\\ x=1.00\end{array}$

Now, put the value of $x=1.00$ in eq. (1):

  $\begin{array}{l}2x+2y=8.80\\ 2\left(1.00\right)+2y=8.80\\ y=\raisebox{1ex}{$6.8$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\\ y=3.4\end{array}$

That means:

The cost of bagels: $x=\$1.00$

The cost of one can of orange juice: $y=\$3.40$

Conclusion:

So, the solution of the equation of system is $x=\$1.00$ and $y=\$3.40$ .