Question

candy crunch
after the costume party, the kids in the class counted their candy. the table represents the pieces of candy each student received. look at the table and answer the questions.
pieces of candy collected at the costume party
100
95
90
85
key: each = 8 students
what does stand for? 13
how many students in all collected either 85 or 90 pieces of candy? 175
how many students collected less than 100 pieces of candy?
how many students in all does the information in the table represent?

Explanation:

Step1: Analyze the key

Each full candy icon = 8 students. For the 90 - piece row, there are 3 full icons and one partial. Let \(x\) be the value of the partial icon. The total for 90 - piece row: \(3\times8 + x\).

Step2: Calculate the value of the partial icon in the 90 - piece row

The total number of students in the 90 - piece row:
We know that for 100 - piece row: \(6\times8=48\) students; 95 - piece row: \(3\times8 = 24\) students; 85 - piece row: \(1\times8=8\) students.
Let's assume the total number of students in the 90 - piece row. Let \(n\) be the number of students in the 90 - piece row.
We know that \(n=3\times8+x\).
Since the pattern of the data (100,95,90,85) is decreasing by 5. But for the number of students, we calculate based on the icon - key.
The total number of students in the table: Let's first calculate for each row.
100 - piece row: \(6\times8 = 48\)
95 - piece row: \(3\times8=24\)
90 - piece row: \(3\times8 + x\)
85 - piece row: \(1\times8 = 8\)

We know that \(90−85 = 5\), \(95 - 90=5\), \(100 - 95 = 5\) (for the candy - piece data). But for the student - count, using the key.
The partial icon:
We know that \(90−85=5\), \(95−90 = 5\), \(100−95=5\) (candy - piece differences). But for the student - count, assume the 90 - piece row: \(3\times8+x\).
Since \(90\) is \(5\) less than \(95\) (in candy - piece), but in terms of student - count, if we assume a linear relationship (not really, but based on the icon key).
The value of the partial icon:
We know that \(90\) - piece row: There are \(3\) full icons (\(3\times8 = 24\)) and one partial.
Let's calculate the total number of students for all rows (assuming we answer the last question first to check consistency, but we'll do it step - by - step.
For the last question (total number of students in the table):
100 - piece row: \(6\times8=48\)
95 - piece row: \(3\times8 = 24\)
90 - piece row: \(3\times8+4=28\) (because \(4\) is half of \(8\), and if we assume a “fair” split for the icon. Since \(90\) is between \(85\) (\(8\) students) and \(95\) (\(24\) students) in a non - linear (icon - based) way. But more accurately, since each icon is \(8\) students. If we assume the partial icon in 90 - piece row is \(4\) (half of \(8\))
85 - piece row: \(1\times8=8\)
Total number of students \(=48 + 24+28 + 8=108\)

For the “less than 100” question:
Students with less than 100 pieces: \(24 + 28+8=60\)

Answer:

1. If the first question (the value of the partial icon in 90 - piece row) is \(4\) (since \(8\div2 = 4\), assuming the partial icon is half of a full icon which represents \(8\) students)
2. Students with 85 or 90 pieces: \((1\times8)+(3\times8 + 4)=8 + 28=36\)
3. Students with less than 100 pieces: \(24+28 + 8=60\)
4. Total number of students: \(48+24 + 28+8=108\)