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

Question

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?

Answer 1

If the numbers can be repeated:
3*(2^8) = 768
3+(2*8) = 19

Answer 2

3+3+3+3+3+2+2=19,
3^5x2^2=972

Answer 3

this suks

Answer 4

this was poster on the day i was born HAHHA

Answer 5

e

Answer 6

Find the product.

13 × (–5) × (–6)

Answer 7

To find the product, we simply multiply the three numbers:

13 × (–5) × (–6) = 390

Answer 8

Find the quotient.

–14 ÷ (–2)

Answer 9

To find the quotient, we simply divide -14 by -2:

-14 ÷ (-2) = 7

Therefore, -14 ÷ (-2) = 7.

Answer 10

Which pair of expressions has the same value?

Answer 11

Without the expressions to compare, I cannot provide a specific answer. Please provide me with the expressions to compare.

Answer 12

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 13

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).

Answer 14

Solve the equation.

–3 + x = 11

Answer 15

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.

Answer 16

Solve the equation.

Q – 26 = –53

Answer 17

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.

Answer 18

Solve the equation.

start fraction lower b over negative 8 end fraction= –2

Answer 19

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.

Answer 20

Solve the equation.

6r = –48

Answer 21

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.

Answer 22

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 23

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.

Answer 24

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 25

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.

Answer 26

Compare. Use < , = , or >.

11 _____ –7

Answer 27

11 > -7

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

So, 11 > -7.

Answer 28

Compare. Use < , = , or >.

11 _____ –7
A. >
B. =
C. <

Answer 29

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

So, 11 > -7.

Therefore, the correct option is (A) >.