1 point - Maribel found a perfectly spherical pumpkin and decided to carve it to create a Jack-O-Lantern. She
hollowed out the pumpkin leaving only the shell which was 3/4 inch thick. Maribel cut and removed pieces of the
pumpkin shell to create the Jack-O-Lantern’s eyes, nose and mouth. For each eye she removed one right triangular
prism with legs measuring 2 inches and 3 inches. For the nose and mouth she removed 10 prisms, each with bases
that were equilateral triangles with side length 1 inch. (a) How many cubic inches of pumpkin shell did Maribel
remove to make the Jack-O-Lantern’s two eyes? Express your answer as a common fraction. (b) How many cubic inches of pumpkin
shell did Maribel remove to make the Jack-O-Lantern’s nose and mouth? Express your answer as a common fraction in simplest
radical form.
2 points - Mr. Thomas returned from his trip to the orchard with a basket of apples. His children went bobbing for
apples, for which they used 16 of the apples. That left Mr. Thomas with only 2/3 the number of apples he
brought back from the orchard. Mr. Thomas decided to use 3/4 of the remaining apples to make 4 apple pies.
Mr. Thomas had just enough apples left to make 2 caramel apples for each of his children. How many children does
Mr. Thomas have?
3 points - On Friday, a house is haunted by a combined total of 51 ghosts, goblins and ghouls, and there were
1/2 as many ghosts as there were goblins. On Saturday, 2/3 of the ghouls each became a ghost. On Sunday, 11
of the ghosts each became a goblin, and the ratio of ghouls to goblins was then 1/3. At that time how many
ghosts were there?