Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5 of what the King had left.
Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes.
Even later, his brother, the second Prince, ate 1/3 of what was then left.
Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants.
How many mangoes were originally in the bowl?
Solution: They royal family started the every with 18 Mangos in the bowl.
Take a look at the student explanations to see how they got the 18. There are some wonderful scores there.
Keep in mind how I am grading your work: your writing, I am posting a rubric for you to judge your work by.
- your ability to be clear in your explanation
- clear about how you got your solution, in other works - your thinking and persistence
- and finally your solution.
(3) Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants.
If 3 were left, that was ½ of the total so 3+3 = 6
(3+3=6) Even later, his brother, the second Prince, ate 1/3 of what was then left.
He ate 1/3rd there was 2/3rds left over. 6=2/3rds so each 1/3rd must equal 3. So, 6+3 = 9.
(6+3=9) Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining
mangos.
He ate 1/4th of what was in the bowl, so what was left when he was done was 3/4ths of mangos. If 9 = 3/4ths , 9/3 (3 parts left) = 3 so each 1/4th must equal 3. So, 9 +3 =12
(12+3=15) Later that same night, the Queen was hungry and couldn't sleep. She, too, found the
mangos and took 1/5 of what the King had left.
She ate 1/5th of what was left from the King’s bowl, so there was 4/5ths left. If you divide 12, what was left over after the king ate his mangos, by 4 total parts that equals 3, so each 1/5ths equaled 3. Therefore if you add 3 to the (4/5ths) what was left in the bowl then , 12+3=15.
(15+3=18) One night the King couldn't sleep, so he went down into the Royal kitchen, where he
found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes.
The king ate 1/6th of the mangos and that means there was 5/6ths leftover. The Queens bowl had a total of15 mangos. 15 = 5/6ths. 15 divided by 5 (the parts left over,) you get 3, so each 1/6th must equal 3. Then, 15 (from the Queens bowl) plus 3 the amount the King eats equals 18.
So, the total pieces of fruit in the bowl to begin with, was 18 mangos.
Another way to look at this is:
Apc p1: I think the oringal amount of mangos is 18 because you can add 1/4 and 1/2
ReplyDeleteCA P1 the answer is 18 thats because every fraction the royal family took was 3, that's if the amount of mangos is 18, 1/6 of 18 is 3 so there's 15 left 1/5 15 is 3, 1/4 of 12 is 3, 1/3 of 9 is 3 and lastly 1/2 of 6 is 3 so it would all be 3. the end number of mangos in there is 18.
ReplyDeleteCA P1 the end answer is 18 the reason is because every amount the royal family took was 3 1/6 of 18 is 3, 1/5 of 15 is 3, 1/4 of 12 is 3, 1/3 of 9 is 3 and lastly 1/2 of 6 is 3. The amount of mangos is 18.
ReplyDelete14, MC Period 3
ReplyDeleteQB per3 10-9-24 the answer is 18
ReplyDeleteM.S Period #6
ReplyDeleteThere were originally 18 mangos because each person takes a fraction of mangos. But for this lets say the number of mangos is x. To explain this, The king takes ⅙ mangos leaving ⅚ mangos in the bowl.Then the queen takes ⅕ leaving ¼ so the equation would be( ⅚)x(⅕)= 9/30 or (3/10)x mangos in the bowl meaning it was(12/30)x left. The first prince takes ¼ which is (12/30)x(¼)=3/10 of x. Now there's (9/30)x mangos left.Now the second prince takes( ⅓) of the mangoes which is (9/30)x(⅓)=1/10 of x. Then do (9/30)x(1/10) to figure out the second prince left (8/30)x mangos left in the bowel.The third prince takes ½ of what mangos was left so (8/30)x(½)= 4/30 or 2/15 of x mangos. So after the third prince there was (8/30)x-(2/15)x =(6/30)x mangos left.Then the servants took (6/30)x mangos that equals ⅕ of mangos.
Therefore ⅙= 3 and 3 x 6=18
18 or 19 mangos I think (I messed up somewhere in the math and Im too lazy to fix it because it took me so long :( Im tired.)
ReplyDelete18
ReplyDelete18
ReplyDelete3 × 2 = 6 mangoes
ReplyDelete6 × (2/3) = 9 mangoes
9 × (4/3) = 12 mangoes
12 × (5/4) = 15 mangoes
15 × (6/5) = 18 mangoes
Originally there was 18 mangoes. (I worked backwards)
AA. per 2.
after the third prince ate 1/2 of what was left, there were 3 mangoes remaining. This means that these 3 mangoes represent the other half of the remaining mangoes. Before the Third Prince: If 3 mangoes are 1/2 of what was left, then the total before the third prince ate would be 3 mangoes * 2 = 6 mangoes. Before the Second Prince: The second prince ate 1/3 of what was left, so 6 mangoes represent 2/3. To find the total before the second prince, we can calculate: 6 mangoes / (2/3) = 9 mangoes. Before the First Prince: The first prince ate 1/4 of what was left, so 9 mangoes represent 3/4. To find the total before the first prince, we can calculate: 9 mangoes / (3/4) = 12 mangoes. Before the Queen: The queen took 1/5 of what was left, so 12 mangoes represent 4/5. To find the total before the queen, we can calculate: 12 mangoes / (4/5) = 15 mangoes. Original Amount: The king took 1/6 of the original amount, so 15 mangoes represent 5/6. To find the original amount, we can calculate: 15 mangoes / (5/6) = 18 mangoes. Therefore, there were originally 18 mangoes in the bowl.
ReplyDeleteJ.S. P6 Initially consider there are 6 parts of mangoes.
ReplyDeleteThe king took 1/6 of the mangoes, so 5 parts are left.
Then, the queen took 1/5 of what the king had left. So remaining is 4 parts.
Then the first prince took 1/4 of the remaining mangoes. So remaining is 3 parts.
Then the second prince took 1/3 of what was then left. So remaining is 2 parts.
Then the third prince took 1/2 of what was left. So remaining is 1 part.
The remaining left part is only three mangoes for the servants.
⇒ 1 part = 3 mangoes
Initially we considered there were 6 parts of mangoes.
Thus, 6 parts = 3(6)
⇒ 18 mangoes
Hence we can conclude that there were initially 18 mangoes in the bowl and it is the only solution.
I believe that the answer is 4. I got this by converting all of the fractions to decimals then adding them including the 3 mangos that was left over. Then I got 4.44 so I rounded down and got 4 as the answer. Ak per3
ReplyDelete1) 18.
ReplyDelete2) I know because I used all the number and simplified it.
3)I put the numbers that came up first in there own equation.
18 mangos
ReplyDeletejf p3.
ReplyDelete1). 18 mangos
2). I took all the numbers and simplified it
3). I did it by putting each number into its own equation
JG p1
ReplyDelete1) 18 mangos
2)i took all the numbers and simplifed it
3)putting each number in its own equation