Algebra world problem

Question

Shandra is on vacation and wants to buy souvenirs for at least eight friends. A postcard book costs $2.50 and a magnet costs $4.00. She can spend up to $30 altogether. Write a system of inequalities to represent the situation. 

Answer 1

We assume here that each friend gets one souvenir. Let x be the number of postcard books and y be the number of magnets purchased. We are told that there are at least 8 friends so that means at least 8 souvenirs and we can write the first inequality as x + y >= 8, i.e. the sum of the numbers of items purchased is greater than or equal to 8.

The second inequality deals with the amount of money available for these purchases (up to $30 for everything). We are told the postcard books cost $2.50 and the magnets cost $4.00 each. From above we know that x is the number of postcard books and y is the number of magnets purchased, so we can multiply the $2.50 by x and $4.00 by y to get the total cost of the items. Since we have to spend less than $30 for everything then we can write the second inequality as 2.50x + 4.00y <= 30.00.

If we rearrange each of these inequalities into the form y = mx + b and plot them on an X-Y plane, we can shade the area where the solutions to both inequalities are valid and identify the acceptable (x, y) pairs, i.e. what values for the number of postcard books and magnets are acceptable.