Question

Santiago is working at his mom's daycare this summer. His mom has asked him to check out the library book sale to look for books they might be able to use in the daycare. When he gets to the book sale, he sees that board books are $4.50 and soft cover books are $1.50. He spends $45

Write a two-variable equation to represent this situation

Let x = number of board books bought
Let y = number of soft cover books bought.

_____________________.


Is it possible that Santiago bought 8 board books and 6 soft cover books? use your equation from part a to check, explain your answer.

(Dropdown 1: yes, no) because (Dropdown 2: when you substitute 8 and 6 into the equation, you get 20, which is less than 45. when you substitute 8 and 6 into the equation, you get 39, which is less than 45. When you substitute 8 and 6 into the equation, you get 45.)


Now describe a graph for the equation you just wrote to graph a solution for it.


What is the minimum number of board books he can buy?
(Dropdown 1: 1, 13, 40, 0.) and the minimum number of softcover books he can buy is (Dropdown 2: 1, 13, 40, 0.)


Choose if the given order pair is a solution to the problem (make sure you consider the constraints)

2, 12 (yes or no)
12, -6 (yes or no)
5.5, 13.5 (yes or no
10, 0 (yes or no)
5, 15 (yes or no)

Answer 1

Equation:
4.50x + 1.50y = 45
(or simplified: 3x + y = 30)

Is (8, 6) possible?
Yes, because when you substitute x = 8 and y = 6 into 4.5x + 1.5y = 45 you get 4.5(8) + 1.5(6) = 36 + 9 = 45.

Graph description:
The graph is a straight line of the equation y = 30 − 3x with x-intercept (10, 0) and y-intercept (0, 30). Valid solutions for the daycare must be nonnegative integers (x, y) on that line (i.e., integer points from x = 0 to x = 10).

Minimum numbers:
Minimum number of board books (x) = 0.
Minimum number of softcover books (y) = 0.

Check ordered pairs (must be nonnegative integers and satisfy the equation):
(2, 12) — No (3·2 + 12 = 18 ≠ 30).
(12, −6) — No (y is negative).
(5.5, 13.5) — No (not whole numbers).
(10, 0) — Yes (3·10 + 0 = 30).
(5, 15) — Yes (3·5 + 15 = 30).