Jacob is buying two kinds of notebooks for school. A spiral notebook costs $2, and a three-ring notebook costs $5. Jacob needs at least six notebooks. The cost of the notebooks can be no more than $20. Write a system, graph, and solve.
+128475 There are only three solutions to this problem......if he only needs a minimum of 6 notebooks.
He can buy no more than 2 of the $5 dollar notebooks. If he bought 3, he wouldn't have enough money for 3 more, even the cheaper ones !!!!
So, let the ordered pair x, y represent the number of $5 notebooks and the number of $2 notebooks, respectively. So we have:
(x, y) = (2, 4) , (1, 5), (0, 6)......and as AT pointed out, buying 6 of the $2 ones would be the cheapest route.
+4473 s = # of spiral notebooks
t = # of three-ring notebooks
$$s + t \ge 6$$
$$2s + 5t \le 20$$
Graph: https://www.desmos.com/calculator/2h6qpiavyo
Note the intersection at (3.333, 2.667).
The region where both inqualities are satisfied is the solution area.
+27 I would like to add to the above answer.
Since you can't have 3.3 or 2.6 notebooks, the highest you could go would be 4 spiral and 2 three-ring notebooks for a total of $18. Or you could just buy 6 spiral notebooks for $12 which would be the most efficient use of the money...
+128475 There are only three solutions to this problem......if he only needs a minimum of 6 notebooks.
He can buy no more than 2 of the $5 dollar notebooks. If he bought 3, he wouldn't have enough money for 3 more, even the cheaper ones !!!!
So, let the ordered pair x, y represent the number of $5 notebooks and the number of $2 notebooks, respectively. So we have:
(x, y) = (2, 4) , (1, 5), (0, 6)......and as AT pointed out, buying 6 of the $2 ones would be the cheapest route.
