Asked by Jarin

the sum of N positive integers is 19. what is the maximum possible product of these N numbers?


thx.

Nice problem.
Let's look at some cases

1. N=2
clearly our only logical choices are 9,10 for a product of 90
It should be obvious that the numbers should be "centrally" positioned
e.g 2 and 17 add up to 19, but only have a product of 34

2. N=3
I considered 4,7,8 for a product of 224, 5,6,8 for a product of 240 and 2,8,9 for a product of only 144.

3. N=4

You should quickly realize that we can't start too high or we will go over 19
so 2,3,4,10 ---> product 240
2,3,5,9 ---> product 270
2,3,6,8 ---> product 288
3,4,5,7 ---> product 420 *!*!

4. N=5

We have to start with 1,2,3 or else we run over,
e.g. if we start with 2,3,4,5 we already have a sum of 14, so we need a 5, but we already used it.

so the only choices would be
1,2,3,4,9 ---> product 216
1,2,3,5,8 ---> product 240
1,2,3,6,7 ---> product 252

so it looks like the 4 numbers 3,4,5,7 which have a sum of 19 and a maximum product of 420 are it!


okay i get it!so you will just have to try out all the possible way!thanks for the help~

Do the numbers have to be different?
Answered by Chris
If the numbers can be repeated:
3*(2^8) = 768
3+(2*8) = 19
Answered by Lisa
3+3+3+3+3+2+2=19,
3^5x2^2=972
Answered by Adisen Hale
this suks
Answered by danny
this was poster on the day i was born HAHHA
Answered by BORN OR POR-
e
Answer
Find the product.

13 × (–5) × (–6)
Answer
Find the quotient.

–14 ÷ (–2)
Answer
Which pair of expressions has the same value?
Answer
Which pair of expressions has the same value?
A. (–2)(–7) and 4 + (–18)
B. (2)(7) and 4 + 18
C. (–2)(7) and 18 + (–4)
D. (2)(–7) and 4 – 18
Answer
Solve the equation.

–3 + x = 11
Answer
Solve the equation.

Q – 26 = –53
Answer
Solve the equation.

start fraction lower b over negative 8 end fraction= –2
Answer
Solve the equation.

6r = –48
Answer
Sarah owns a small business. There was a loss of $19 on Thursday and a loss of $12 on Friday. On Saturday there was a loss of $11, and on Sunday there was a profit of $15. Find the total profit or loss for the four days.
Answer
Sarah owns a small business. There was a loss of $19 on Thursday and a loss of $12 on Friday. On Saturday there was a loss of $11, and on Sunday there was a profit of $15. Find the total profit or loss for the four days.
A. $35 loss
B. $19 profit
C. $27 loss
D. $57 profit
Answer
Compare. Use < , = , or >.

11 _____ –7
Answer
Compare. Use < , = , or >.

11 _____ –7
A. >
B. =
C. <
Answered by Bot
To find the product, we simply multiply the three numbers:

13 × (–5) × (–6) = 390
Answered by Bot
To find the quotient, we simply divide -14 by -2:

-14 ÷ (-2) = 7

Therefore, -14 ÷ (-2) = 7.
Answered by Bot
Without the expressions to compare, I cannot provide a specific answer. Please provide me with the expressions to compare.
Answered by Bot
Let's simplify each expression to determine which pair has the same value:

A. (-2)(-7) = 14 and 4 + (-18) = -14, so A is not the correct answer.

B. (2)(7) = 14 and 4 + 18 = 22, so B is not the correct answer.

C. (-2)(7) = -14 and 18 + (-4) = 14, so C is the correct answer.

D. (2)(-7) = -14 and 4 - 18 = -14, so D is not the correct answer.

Therefore, the pair of expressions that has the same value is C, (-2)(7) and 18 + (-4).
Answered by Bot
To solve for x, we want to isolate x on one side of the equation. First, we add 3 to both sides of the equation to cancel out the -3 on the left side:

-3 + x + 3 = 11 + 3

Simplifying the left side, we get:

x = 14

Therefore, the solution to the equation -3 + x = 11 is x = 14.
Answered by Bot
To solve for Q, we want to isolate Q on one side of the equation. First, we add 26 to both sides of the equation to cancel out the -26 on the left side:

Q - 26 + 26 = -53 + 26

Simplifying the right side, we get:

Q = -27

Therefore, the solution to the equation Q - 26 = -53 is Q = -27.
Answered by Bot
To solve for b, we want to isolate b on one side of the equation. First, we multiply both sides of the equation by -8 to cancel out the fraction on the left side:

(-8) * start fraction lower b over negative 8 end fraction = -2 * (-8)

Simplifying the left side, we get:

b = 16

Therefore, the solution to the equation start fraction lower b over negative 8 end fraction = –2 is b = 16.
Answered by Bot
To solve for r, we want to isolate r on one side of the equation. First, we divide both sides of the equation by 6:

6r/6 = -48/6

Simplifying, we get:

r = -8

Therefore, the solution to the equation 6r = -48 is r = -8.
Answered by Bot
To find the total profit or loss for the four days, we need to add up the losses and profits for each day:

Loss on Thursday = $19
Loss on Friday = $12
Loss on Saturday = $11
Profit on Sunday = $15

To find the total profit or loss, we add up the amounts:

Total profit/loss = -19 - 12 - 11 + 15
Total profit/loss = -27 + 15
Total profit/loss = -12

Therefore, the total profit or loss for the four days is a loss of $12.
Answered by Bot
To find the total profit or loss for the four days, we need to add up the losses and profits for each day:

Loss on Thursday = $19
Loss on Friday = $12
Loss on Saturday = $11
Profit on Sunday = $15

To find the total profit or loss, we add up the amounts:

Total profit/loss = -19 - 12 - 11 + 15
Total profit/loss = -27 + 15
Total profit/loss = -12

Therefore, the total profit or loss for the four days is a loss of $12.

So, the correct option is (C) $27 loss.
Answered by Bot
11 > -7

Therefore, the correct symbol to fill in the blank is >.

So, 11 > -7.
Answered by Bot
As 11 is greater than -7, the correct symbol to fill in the blank is >.

So, 11 > -7.

Therefore, the correct option is (A) >.