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?
how many students in all collected either 85 or 90 pieces of candy?
how many students collected less than 100 pieces of candy?
how many students in all does the informati in the table represent?

Explanation:

Step1: Find the value of the incomplete candy icon

For the 90 - piece row, there are 4 candy icons (3 complete and 1 incomplete). Let \(x\) be the value of the incomplete icon. We know that each complete icon is 8 students. The total for the 90 - piece row: \(3\times8 + x\).
We can also calculate the total number of students in another way.
Let's first consider the total number of students in each row:

• For 100 pieces: \(5\times8=40\) students
• For 95 pieces: \(3\times8 = 24\) students
• For 85 pieces: \(1\times8=8\) students

Let the total number of students in the 90 - piece row be \(y\).

We know that the key is based on a consistent value for each icon.

Let's assume the total number of students in the 90 - piece row. We know that \(y\) should follow a pattern. Let's use the fact that the difference between 95 and 90 is 5, and between 90 and 85 is 5.

We can also use the proportion. Since each complete icon is 8 students, and assume the incomplete icon is \(x\) students.

We know that \(3\times8+x\) (for 90 - piece row) and we can find \(x\) by considering the total number of students in all rows.

Another way:
The total number of complete icons: \(5 + 3+3 + 1=12\) complete icons (counting 3 for 90 - piece row as complete - like in terms of calculation unit).
Let's assume the value of the incomplete icon.
We know that \(90\) - piece row: Let the total number of students in 90 - piece row be \(n\).
We know that \(n=3\times8 + x\).
We also know that if we consider the total number of students in all rows (except 90 - piece row) is \(40+24 + 8=72\) students.
Let's assume the total number of students in 90 - piece row.
We know that \(x = 4\) (because \(3\times8+4=28\) and if we check the pattern: 100 - piece row (40), 95 - piece row (24), 90 - piece row (28 is wrong, no). Wait, another approach:
The total number of students in 100 - piece row: \(5\times8 = 40\)
In 95 - piece row: \(3\times8=24\)
In 85 - piece row: \(1\times8 = 8\)
Let the number of students in 90 - piece row be \(n\).
We know that \(n=3\times8+x\).
We also know that if we assume the total number of students in all rows (including 90 - piece row) is \(T\).
Let's use the fact that the difference between 100 and 95 is 5 (in candy pieces), 95 and 90 is 5, 90 and 85 is 5.
The number of students in 90 - piece row:
We know that \(3\times8+x\). Since \(90\) - piece row: if we assume \(x = 4\) (because \(3\times8+4=28\) and \(40+24+28 + 8=100\) (total number of students).

Step2: Calculate the number of students who collected 85 or 90 pieces

For 85 pieces: \(1\times8 = 8\) students
For 90 pieces: \(3\times8+4=28\) students
Total: \(8 + 28=36\) students

Step3: Calculate the number of students who collected less than 100 pieces

Number of students who collected 100 pieces: \(5\times8=40\)
Total number of students in all rows: \(40+24+28 + 8=100\)
Number of students who collected less than 100 pieces: \(100 - 40=60\)

Step4: Calculate the total number of students

Total number of students: \(5\times8+3\times8+(3\times8 + 4)+1\times8\)

$$=(5 + 3+3 + 1)\times8+4$$

$$=12\times8+4$$

$$=96 + 4=100$$

Answer:

1. The incomplete candy icon stands for \(4\) students.
2. \(36\) students collected either 85 or 90 pieces of candy.
3. \(60\) students collected less than 100 pieces of candy.
4. The table represents \(100\) students in total.