Chapter 8, Problem 31CCSR

(a)

To determine

Towrite the linear equations to solve the problem.

Answer to Problem 31CCSR

the system of linear equation is $x+y=87$ and $1.5x+.5y=78.50$

Explanation of Solution

Given Information:The cost of one hot dog $\$1.50$

The cost of one soda = $\$1.50$

Total money earned = $\$78.50$

Total hot dog and soda sold = $87$

Calculations:

Let $x$ be the number of hot dogs sold.

Let $y$ be the number of sodas sold.

According to total number of hot dog and sodas sold, the equation is $x+y=87$

According to the costs, the equation is $1.5x+.5y=78.50$

Therefore, the system of linear equation is $x+y=87$ and $1.5x+.5y=78.50$

(b)

To determine

To calculate: To find the number of hot dogs and sodas sold.

Answer to Problem 31CCSR

The number of hot dogs sold is $35$ .

The number of sodas sold is $52$

Explanation of Solution

Given Information:The cost of one hot dog $\$1.50$

The cost of one soda = $\$1.50$

Total money earned = $\$78.50$

Total hot dog and soda sold = $87$

the system of linear equation is $x+y=87$ and $1.5x+.5y=78.50$

Calculations:

The system of linear equation is $x+y=87$ …… (1)

  $1.5x+.5y=78.50$  ...... (2)

Multiply (1) by $1.5$ and write as follows

  $1.5x+1.5y=130.5$  ...... (3)

  $1.5x+.5y=78.50$  ...... (4)

Subtract (4) from (3)

  $y=52$

Substitute the value $y=52$ in (1) to get the value of $x$

  $\begin{array}{c}x+52=87\\ x=87-52\\ =35\end{array}$

The number of hot dogs sold is $35$ .

The number of sodas sold is $52$