Laura is building wooden crates to organize the items in her shed. She has 200 nails she can use. A small crate requires 12 nails, while a big crate requires 24 nails.
If s represents the number of small crates Laura builds and b represents the number of big crates she builds, which inequality describes this situation?
Which pairs (s,b) represent possible numbers of small and big crates Laura could build? Select all that apply.
10,5
9,3
3,7
7,4
3,5
8,8
The inequality that describes this situation is 12s + 24b <= 200.
To find the pairs (s,b) that represent possible numbers of small and big crates Laura could build, we can plug in the values into the inequality and see if they satisfy it:
1. 10 small crates and 5 big crates:
12(10) + 24(5) = 120 + 120 = 240, does not satisfy the inequality.
2. 9 small crates and 3 big crates:
12(9) + 24(3) = 108 + 72 = 180, satisfies the inequality.
3. 3 small crates and 7 big crates:
12(3) + 24(7) = 36 + 168 = 204, does not satisfy the inequality.
4. 7 small crates and 4 big crates:
12(7) + 24(4) = 84 + 96 = 180, satisfies the inequality.
5. 3 small crates and 5 big crates:
12(3) + 24(5) = 36 + 120 = 156, satisfies the inequality.
6. 8 small crates and 8 big crates:
12(8) + 24(8) = 96 + 192 = 288, does not satisfy the inequality.
Therefore, the pairs (s,b) that represent possible numbers of small and big crates Laura could build are:
- 9,3
- 7,4
- 3,5