Question

Larry has a gift card worth 400 for a local entertainment store Movies cost $20 each and newly released video games cost $50 each. In order to use the gift card, Larry must purchase at least nine items. Which is a combination of movies and newly released video games that Larry could purchase using his gift card?A: (5, 6)B:(10, 4)C: (20,0)D:(15, 2)

Answer 1

All are correct.

Explanation:

Let x be the number of movies and y be the number of newly released video games.

Larry has a gift card worth 400 for a local entertainment store Movies cost $20 each and newly released video games cost $50 each.

`20x+50y\leq 400`

Larry must purchase at least nine items.

`x+y\geq 9`

Check both inequalities of all given ordered pairs.

For (5,6),

`20(5)+50(6)\leq 400\Rightarrow 400\leq 400`

`5+6\geq 9\Rightarrow 16\geq 9`

Point (5,6) satisfy both inequalities.

For (10,4),

`20(10)+50(4)\leq 400\Rightarrow 400\leq 400`

`10+4\geq 9\Rightarrow 14\geq 9`

Point (10,4) satisfy both inequalities.

For (20,0),

`20(20)+50(0)\leq 400\Rightarrow 400\leq 400`

`20+0\geq 9\Rightarrow 20\geq 9`

Point (20,0) satisfy both inequalities.

For (15,2),

`20(15)+50(2)\leq 400\Rightarrow 400\leq 400`

`15+2\geq 9\Rightarrow 17\geq 9`

Point (15,2) satisfy both inequalities.

Therefore, all combination of movies and newly released video games Larry could purchase using his gift card.