Question

Julian spent $15.00 to purchase some notebooks that cost $3.50 each and some pens that cost $4.50 each. Assuming he bought at least one notebook, what is the greatest number of pens Julian could have purchased?

Answer 1

Answer:  The greatest number of pen Julian could have purchased is 2.

Step-by-step explanation:  Given that Julian spent $15.00 to purchase some notebooks that cost $3.50 each and some pens that cost $4.50 each.

We are to find the greatest number of pens Julian could have purchased is he bought at least one notebook.

Let x and y represents the number of notebooks and numbers of pen respectively that Julian bought.

Then, according to the given information, we have

$3.50x+4.50y=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since Julian bought at least 1 notebook, so

$x\geq 1\\\\\Rightarrow 1\leq x.$

Therefore, from equation (i), we get

$3.50\times 1+4.50y\leq 15\\\\\Rightarrow 3.50+4.50y\leq 15\\\\\Rightarrow 4.50y\leq 15-3.50\\\\\Rightarrow 4.50y\leq11.50\\\\\Rightarrow y\leq \dfrac{11.50}{4.50}\\\\\Rightarrow y\leq 2.55.$

Thus, the greatest number of pen Julian could have purchased is 2.