Use the tables to answer the question
Sonia
Number of Problems Minutes of Writing
120
25
360
500
60
1,200
Maryna
Number of Problems Minutes of Writing
200
15
375
500
1,250
Based on the tables showing the number of minutes two different lessons, who spent writing math problems for two different lessons, who spent more time writing per problem? Write the answer in unit rate form.
a. Sonia spent the same amount of time as Maryna time writing per problem at the unit rate of 25 minutes/1 problem.
b. Maryna spent less time writing per problem at the at the unit rate of 1 minute/25 problem.
c. Maryna spent more time writing per problem at the unit rate of 25 minutes/1 problem.
d. Sonia spent more time writing per problem at the unit rate of 20 minutes/1 problem.
c. Maryna spent more time writing per problem at the unit rate of 25 minutes/1 problem.
To find out who spent more time writing per problem, we need to calculate the unit rate for each person. The unit rate is the number of minutes spent writing per problem.
For Sonia:
- Number of problems: 120, 360, 500
- Minutes of writing: 25, 60, 1,200
To find the unit rate, divide the minutes of writing by the number of problems for each set of data:
- For the first set: 25 minutes / 120 problems = 0.2083 minutes/problem (rounded to 4 decimal places)
- For the second set: 60 minutes / 360 problems = 0.1667 minutes/problem (rounded to 4 decimal places)
- For the third set: 1,200 minutes / 500 problems = 2.4 minutes/problem
For Maryna:
- Number of problems: 200, 375, 500
- Minutes of writing: 15, 500, 1,250
Again, calculate the unit rate by dividing the minutes of writing by the number of problems for each set of data:
- For the first set: 15 minutes / 200 problems = 0.075 minutes/problem
- For the second set: 500 minutes / 375 problems = 1.3333 minutes/problem (rounded to 4 decimal places)
- For the third set: 1,250 minutes / 500 problems = 2.5 minutes/problem
Comparing the unit rates, we can see that:
- For Sonia: the unit rates are 0.2083 minutes/problem, 0.1667 minutes/problem, and 2.4 minutes/problem.
- For Maryna: the unit rates are 0.075 minutes/problem, 1.3333 minutes/problem, and 2.5 minutes/problem.
Therefore, we can conclude that Maryna spent more time writing per problem at a unit rate of 2.5 minutes/1 problem.
So, the correct answer is:
c. Maryna spent more time writing per problem at the unit rate of 25 minutes/1 problem.