Question

You have $\$5.60$ to buy avocados for a guacamole recipe. Avocados cost $\$1.40$ each.
a. Write and solve an inequality that represents the numbers of avocados you can buy.
b. Are there infinitely many solutions in this context? Explain.

Answer 1

Step 1 : Write and solve the inequality

Given:

$$\begin{gathered} Amountofmoneyyouhave=\$5.60 \\ Eachavocado\cos t=\$1.40 \end{gathered}$$

Let, the number of avocados that you can buy be $x$.

So, according to the question.

Required inequality is $1.40\times x\le 5.60$

Now,

$$\begin{gathered} \Rightarrow 1.40x\le 5.60 \\ \Rightarrow x\le \frac{5.60}{1.40} \\ \therefore x\le 4 \end{gathered}$$

Hence, you can buy a maximum of $4$ avocados.

Step 2 : Find the number of solution

As the number of avocados can only be a positive integer less than or equal to $4$.

So, possible number of avocados that he can buy are $1,2,3$ or $4$.

Hence, there are only finite solution in this context.