Chapter 5.4, Problem 25E

To determine

To calculate:

System of linear equation to find the piece of $1$ cup of dried fruit and $1$ cup of almonds.

Answer to Problem 25E

The cups of dried fruit are free and $1$ cup of almond cots $1.5\$$ .

Explanation of Solution

Given information:

Price of small bag is $\$6$ .

Price of big bag is $\$9$

Calculation:

Lets,

  $f=$ Price of $1$ cup of dried fruit.

  $a=$ Price of $1$ cup of almonds.

For getting linear system, consider that the total price of bag is given by sum of the price of cups times the number of cups in each bag.

Thus,

  $\{\begin{array}{l}3f+4a=6\\ 41/2f+6a=9\end{array}$

Solve for $a$ in first equation:

  $a=\left(6-3f\right)/4$

Put in second equation,

  $\begin{array}{l}41/2f+6.\left(6-3f\right)/4=9\\ 41/2f+9-9/2f=9\\ 16f=0\\ f=0\end{array}$

Now, put this value in formula found for $a$ ,

  $\begin{array}{l}a=\left(6-3.0\right)/4\\ =3/2\\ =1.5\end{array}$

Hence, the cups of dried fruit are free and $1$ cup of almond cots $1.5\$$ .