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.
a. How many rows were empty on the first train? How many additional riders would it take to fill the empty rows? Explain your answer.
b.How many rows were empty on the third train? How many additional riders would it take to fill the empty rows? Explain your answer.
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7 1/4 * 4 = 29 seats filled
5 1/2 * 4 = 22
so 1 1/4 rows were empty
Was that on a or b?
And also, you were supposed to do both.
Can you please use more appropriate first names, especially considering you are posting on an educational website? I have replaced the name you used with a previous (and more appropriate) name that you used. Thank you.
Sure, I can help you with these questions!
a. To find out how many rows were empty on the first train, we need to subtract the number of filled rows from the total number of rows. The first train has 8 rows, and the operators reported that 7 1/4 rows were filled.
To subtract a fraction, we need a common denominator. In this case, the common denominator is 4. So, we convert 7 1/4 to a fraction with a denominator of 4:
7 1/4 = (7 * 4 + 1) / 4 = 29 / 4
Now, we can subtract the filled rows from the total number of rows:
Empty rows on the first train = Total rows - Filled rows
Empty rows on the first train = 8 - 29/4
To subtract fractions, we again need a common denominator:
Empty rows on the first train = (8 * 4) / 4 - (29 / 4)
Empty rows on the first train = 32/4 - 29/4
Empty rows on the first train = 3/4
Therefore, there are 3/4 of a row empty on the first train.
To calculate how many additional riders would it take to fill the empty rows, we need to find the number of riders that can fill 3/4 of a row. Each row can hold 4 riders, so to find the number of riders for 3/4 of a row, we multiply 4 by 3/4:
Additional riders needed to fill empty rows on the first train = 4 * 3/4
Additional riders needed to fill empty rows on the first train = 3
So, it would take 3 additional riders to fill the empty rows on the first train.
b. Similarly, to find out how many rows were empty on the third train, we subtract the number of filled rows from the total number of rows. The third train has 8 rows, and the operators reported that 5 1/2 rows were filled.
To subtract a fraction, we need a common denominator. In this case, the common denominator is 2. So, we convert 5 1/2 to a fraction with a denominator of 2:
5 1/2 = (5 * 2 + 1) / 2 = 11 / 2
Now, we can subtract the filled rows from the total number of rows:
Empty rows on the third train = Total rows - Filled rows
Empty rows on the third train = 8 - 11/2
To subtract fractions, we again need a common denominator:
Empty rows on the third train = (8 * 2) / 2 - (11/2)
Empty rows on the third train = 16/2 - 11/2
Empty rows on the third train = 5/2
Therefore, there are 5/2 of a row empty on the third train.
To calculate how many additional riders would it take to fill the empty rows, we need to find the number of riders that can fill 5/2 of a row. Each row can hold 4 riders, so to find the number of riders for 5/2 of a row, we multiply 4 by 5/2:
Additional riders needed to fill empty rows on the third train = 4 * 5/2
Additional riders needed to fill empty rows on the third train = 10
So, it would take 10 additional riders to fill the empty rows on the third train.
I hope this explanation helps! Let me know if you have any more questions.