Chapter 4.5, Problem 55PPS

(a)

To determine

To find: The number of drinks was sold.

Answer to Problem 55PPS

The person sold 325 medium drinks, 650 small drinks and 410 large drinks.

Explanation of Solution

Given,

The number of drinks is expressed as,

  $\begin{array}{l}x+2x+y=1385\\ 3x+y=1385\end{array}$

Here, x is the number of medium drinks, 2x is the number of small drinks and y is the number of large drinks.

The total sales is written as,

  $\begin{array}{l}1.75x+1.15\left(2x\right)+2.25y=2238.75\\ 4.05x+2.25y=2238.75\end{array}$

Calculation:

Calculate the value of x using the Cramer’s rule.

  $\begin{array}{c}x=\frac{\left|\begin{array}{cc}1385& 1\\ 2238.75& 2.25\end{array}\right|}{\left|\begin{array}{cc}3& 1\\ 4.05& 2.25\end{array}\right|}\\ =\frac{1385\left(2.25\right)-\left(2238.75\right)\left(1\right)}{3\left(2.25\right)-4.05\left(1\right)}\\ =\frac{877.5}{2.7}\\ =325\end{array}$

Calculate the value of y using the Cramer’s rule.

  $\begin{array}{c}y=\frac{\left|\begin{array}{cc}3& 1385\\ 4.05& 2238.75\end{array}\right|}{\left|\begin{array}{cc}3& 1\\ 4.05& 2.25\end{array}\right|}\\ =\frac{3\left(2238.75\right)-4.05\left(1385\right)}{3\left(2.25\right)-4.05\left(1\right)}\\ =\frac{1107}{2.7}\\ =410\end{array}$

Thus, the person sold 325 medium drinks, 650 small drinks and 410 large drinks.

(b)

To determine

To find: The sale for that week.

Answer to Problem 55PPS

The sale for that week is $2426.25.

Explanation of Solution

Calculate the total sale for that week.

  $\begin{array}{c}\text{Total sales}=\text{sale of small drink}+\text{same of medium drink}+\text{sale of large drink}\\ =1.25\left(650-140\right)+1.75\left(325+125\right)+2.25\left(410+35\right)\\ =637.50+787.50+1001.25\\ =\$2426.25\end{array}$

Thus, the sale for that week is $2426.25.

(c)

To determine

To find: The reason whether it was a good business move for the vendor to raise the price of small drink.

Answer to Problem 55PPS

Yes, it was a good move to raise the price of small drink.

Explanation of Solution

It was good move to raise the price of small drink for the vendor as he sold 140 smaller drinks, so that he sold 125 medium drinks more and 35 large drink more.

So, he made the profit of $187.50.