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.

Question

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?
a) 12s + 24b > or equal to 200
b) 12s + 24b < or equal to 200
c) 24s +12b < or equal to 200
d) 24s + 12b> or equal to 200

Which pairs (s,b) represent possible numbers of small and big crates Laura could build? Select all that apply.
a) (10,5)
b) (8,8)
c) (3,5)
d) (7,4)
e) (3,7)
f) (9,3)

Answer 1

The correct inequality is:

a) 12s + 24b <= 200

Now we can test the pairs:

a) (10,5): 12(10) + 24(5) = 120 + 120 = 240. This pair does not satisfy the inequality.
b) (8,8): 12(8) + 24(8) = 96 + 192 = 288. This pair does not satisfy the inequality.
c) (3,5): 12(3) + 24(5) = 36 + 120 = 156. This pair satisfies the inequality.
d) (7,4): 12(7) + 24(4) = 84 + 96 = 180. This pair satisfies the inequality.
e) (3,7): 12(3) + 24(7) = 36 + 168 = 204. This pair does not satisfy the inequality.
f) (9,3): 12(9) + 24(3) = 108 + 72 = 180. This pair satisfies the inequality.

Therefore, the possible pairs that represent the numbers of small and big crates Laura could build are:

c) (3,5)
d) (7,4)
f) (9,3)