Chapter 8, Problem 23SGR

To determine

To find: two solutions of the given equation

Answer to Problem 23SGR

The solution $\left(0,4\right)$ means that L can buy 0 small smoothies and 4 large smoothies with $12.

And, the solution $\left(6,1\right)$ means that L can buy 6 small smoothies and 1 large smoothie with $12.

Explanation of Solution

Given:

  $1.5x+3y=12$

Cost of small smoothie (x) is $1.50

Cost oflarge smoothie (y) is $3

Calculation:

Subtract both sides of equation by $1.5x$ to separate the variable y

  $\begin{array}{c}1.5x+3y-1.5x=12-1.5x\\ 3y=12-1.5x\end{array}$

Divide both sides of equation by 3.

  $\begin{array}{c}\frac{3y}{3}=\frac{12-1.5x}{3}\\ y=4-0.5x\end{array}$

Thus, take different value of x and solve for y

Put $x=0$ in equation.

  $\begin{array}{c}y=4-0.5\left(0\right)\\ =4\end{array}$

Now, put $x=6$ in equation.

  $\begin{array}{c}y=4-0.5\left(6\right)\\ =4-3\\ =1\end{array}$

Hence, the two solutions of the equation $1.5x+3y=12$ is $\left(0,4\right),\left(6,1\right)$

Conclusion:

Therefore, the solution $\left(0,4\right)$ means that L can buy 0 small smoothies and 4 large smoothies with $12.

And, the solution $\left(6,1\right)$ means that L can buy 6 small smoothies and 1 large smoothie with $12.