A roller coaster has 3 trains with 8 rows per train. Riders stand in rows of 4, for a total of 32 rider per train. The operators of the coaster recorded the number of riders on each train during a run. On the first train, the operators reported that 7 1/4 rows were filled. On the second train, all 8 rows were filled, and on the third train, 5 1/2 rows were filled.
1. Evaluate How many more rows were filled on the first train than on the third train?
2. Multi-Step How many rows were empty on the first train? How many additional rider would it take to fill the empty rows? Explain your answer.
3. Multi-Step How many rows were empty on the third train? How many additional riders would it take to fill the empty rows? Explain your answer.
a. 1 row
b. 6 people
Step-by-step explanation:
a. Each train has 7 rows yet the first train only had 6 rows filled up. This means that:
= 7 - 6
= 1 row was empty
b. Riders stand in rows of 6 which means that one row has 6 people. With only 1 row empty, the number of people needed will be:
= 6 people i hope this helps man
Well what about the third question?
Plus where did you get 6
To answer the questions, let's break down the information provided in the problem:
1. The first train had 7 1/4 rows filled, and the third train had 5 1/2 rows filled.
To find the difference in the number of rows filled on the first and third trains, we subtract the number of rows filled on the third train from the number of rows filled on the first train:
7 1/4 - 5 1/2
To subtract these mixed numbers, we need to convert them to improper fractions:
7 1/4 = 29/4
5 1/2 = 11/2
Now we can subtract the fractions:
29/4 - 11/2
To subtract fractions, we need a common denominator. The least common multiple (LCM) of 4 and 2 is 4. We can rewrite the fractions with a common denominator:
29/4 - 11/2 = 29/4 - (11/2) * (2/2) = 29/4 - 22/4
Now, subtract the fractions:
29/4 - 22/4 = (29 - 22)/4 = 7/4
Therefore, there were 7/4 or 1 3/4 more rows filled on the first train than on the third train.
2. To determine how many rows were empty on the first train, we need to subtract the number of filled rows from the total number of rows:
Total rows - Filled rows
Total rows = 8
Filled rows = 7 1/4
We can convert 7 1/4 to an improper fraction:
7 1/4 = 29/4
Now, subtract:
8 - 29/4
To subtract a whole number from a fraction, we need to rewrite the whole number as a fraction with the same denominator:
8 = 8/1
Now, subtract the fractions:
8/1 - 29/4
To subtract fractions, we need a common denominator. The common denominator here is 4. Rewrite the fractions:
8/1 - 29/4 = 8/1 - (29/4) * (4/4) = 8/1 - 116/4
Now, subtract the fractions:
8/1 - 116/4 = (8 - 116)/4 = -108/4
-108/4 is an improper fraction. To simplify it, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
-108/4 = -27/1
Therefore, there were 27 empty rows on the first train.
To determine how many additional riders would it take to fill the empty rows, we need to multiply the number of empty rows by the number of riders per row:
27 * 4 = 108
It would take 108 additional riders to fill the empty rows on the first train.
3. To determine how many rows were empty on the third train, we need to subtract the number of filled rows from the total number of rows:
Total rows - Filled rows
Total rows = 8
Filled rows = 5 1/2
We can convert 5 1/2 to an improper fraction:
5 1/2 = 11/2
Now, subtract:
8 - 11/2
To subtract a fraction from a whole number, we need to rewrite the whole number as a fraction with the same denominator:
8 = 8/1
Now, subtract the fractions:
8/1 - 11/2
To subtract fractions, we need a common denominator. The common denominator here is 2. Rewrite the fractions:
8/1 - 11/2 = 8/1 - (11/2) * (2/2) = 8/1 - 22/2
Now, subtract the fractions:
8/1 - 22/2 = (8 - 22)/2 = -14/2
-14/2 is an improper fraction. To simplify it, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
-14/2 = -7/1
Therefore, there were 7 empty rows on the third train.
To determine how many additional riders would it take to fill the empty rows, we need to multiply the number of empty rows by the number of riders per row:
7 * 4 = 28
It would take 28 additional riders to fill the empty rows on the third train.