Question

During the month of January, Fransworth Computer Center sold 24 computers of a certain model and 40 companion printers. The total sales in these two items for the month of January was $38,736. In February they sold 30 of the computers and 50 printers.

A. Assuming the prices stayed constant during the months of January and
February, is it possible that their February sales could have totaled $51,470
on these two items? Explain.

B. Assuming the prices stayed constant during the months of January and
February, is it possible that their February sales could have totaled $48,420
on these two items? Explain.

Answer 1

see the explanation

Explanation:

Let

x ------> the price of one computer

y -----> the price of one printer

we know that

Month of January

24x+40y=38,736 -----> equation A

In February they sold 30 of the computers and 50 printers.

Divide 30 by 24 -----> 30/24=1.25

Divide 50 by 40 -----> 50/40=1.25

That means ----> The quantity sold in February represents an additional 25% of the quantity sold in January.

therefore

If prices remain the same, total February sales will equal January sales increased by 25%.

so

Month of February

30x+50y=(1.25)38,736

30x+50y=48,420

Part A) Assuming the prices stayed constant during the months of January and February, is it possible that their February sales could have totaled $51,470 on these two items?

Is not possible, because assuming the prices stayed constant during the months of January and February, the total sales could have totaled $48,420 on these two items (see the procedure)

Part B) Assuming the prices stayed constant during the months of January and February, is it possible that their February sales could have totaled $48,420 on these two items?

Yes, it is possible (see the procedure)