Taro and Jiro respectively decided to make a plan to do homework of the mathematics of the summer vacation.
Taro decided to solve three problems a day from the first day of the summer vacation.
Jiro decided not do its homework for six days of the beginning of the summer vacation and from seventh day to solve [ ] problems a day until he finish the homework.
It was found that several days after Jiro started to solve, the number of problems solved by Taro and Jiro are the same.
Since the day above Taro solved five problems a day until the day he would finish, but it was two days after the day Jiro finished that Taro finished.
The number of days that Taro solved three problems a day is same as the number of days Jiro solved five days a day.
Answer the following questions.
(1) How many days did Taro take to finish the homework?
(2) How many days did Jiro take to finish the homework?
(3) Find the number applied in [ ].
Taro decided to solve three problems a day from the first day of the summer vacation.
Jiro decided not do its homework for six days of the beginning of the summer vacation and from seventh day to solve [ ] problems a day until he finish the homework.
It was found that several days after Jiro started to solve, the number of problems solved by Taro and Jiro are the same.
Since the day above Taro solved five problems a day until the day he would finish, but it was two days after the day Jiro finished that Taro finished.
The number of days that Taro solved three problems a day is same as the number of days Jiro solved five days a day.
Answer the following questions.
(1) How many days did Taro take to finish the homework?
(2) How many days did Jiro take to finish the homework?
(3) Find the number applied in [ ].
Answer
(1) 16 days
(2) 24 days
(3) six
Solution
(1) The number of days (first half) that Taro solved five a day is same as the number of days (second half) that Taro solved five a day.
In addition, Taro and Jiro solved the number of the same problems at the time of the end in the first half.
(2) 24 days
(3) six
Solution
(1) The number of days (first half) that Taro solved five a day is same as the number of days (second half) that Taro solved five a day.
In addition, Taro and Jiro solved the number of the same problems at the time of the end in the first half.
Based on these statements, it is found that the ratio of the number of the problems solved B in first half and second half is 3 : 5 and the ratio of numbers Jiro solved in first half and second half is also 3 : 5.
As the number of problems Jiro solved a day is same through days, the ratio of days of A : B that is the ratio of days Jiro solved is 3 : 5 in the figure.
As the number of problems Jiro solved a day is same through days, the ratio of days of A : B that is the ratio of days Jiro solved is 3 : 5 in the figure.
As A + 6 = B + 2, the difference between A and B are 6 - 2 = 4 days.
4 days is equivalent to 5 -3 =2 which is the differences of the ration.
Thus, the ratio 1 is equivalent to 2 days (4 days / 2 = 2).
4 days is equivalent to 5 -3 =2 which is the differences of the ration.
Thus, the ratio 1 is equivalent to 2 days (4 days / 2 = 2).
Therefore, the days Jiro solved problems are 2 days × (3 + 5) = 16 days.
(2) Taro took eight days (6+2=8) more than Jiro.
It is 16 + 8 = 24days.
(3) Total number of problems is = (3 + 5) × 12 days = 96 problems.
Since Jiro solved 96 problems 16 days, the number solved per day is 96 / 16 = 6.
