Question

What two numbers have the product of 234 and the sum of 31

Answer 1

the product of 2, 3, and 4?

can you elaborate a little bit more please. and Welcome to open study

Answer 2

I think the question might be typed in a bit wrong, not sure , can you check on that please

Answer 3

No I just checked and couldn't get the answer

Answer 4

ok, i see what they want.

Answer 5

define two variables for your two unknown numbers, let them be X and Y

The sum of the two numbers x and y are 31

X + Y = 31

The Product of x and y is 234

X * Y = 234

Answer 6

You now have 2 equations, with two unknown variables, it is possible to solve these for X and Y

Answer 7

X + Y = 31
X * Y = 234

Answer 8

Do you know where to begin here?

Answer 9

Yes that's the equation but they need to have the same 2 numbers and that's whats I cant get

Answer 10

right, we need to find a value for x and y, so that both those equations are true

Answer 11

to start, solve
X+ Y = 31 for X to get

X = 31 - Y

Answer 12

Now you can substitute that X = 31 - Y into the second equation like this

X*Y = 234

(31 - Y)*Y = 234

31Y - Y^2 = 234

Y^2 - 31Y + 234 = 0

(Y-18)(Y-13) = 0

Answer 13

i distributed the left side, and then moved it all to one side and factored into the two parenthesis terms,
So now you have

(Y-18)(Y-13)=0 which means either one of those can be zero

Y-18 = 0
Y - 13 = 0

Y = 13 OR Y=18

Answer 14

Oh my gosh thank you so much!!!

Answer 15

If Y=13
Then from equation 1, X+ Y = 31

X + 13 = 31

X = 31 - 13 = 18

Answer 16

SO the choices are

X=13, Y=18
Or
X=18 , Y = 13

Answer 17

The two numbers are 13 and 18

Answer 18

U understand how the equations were pulled from the problem
X + Y = 31
X*Y = 234

Answer 19

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In the question type @DanJS

Answer 20

Thank your i did

Answer 21

You

Answer 22

another way

234=2*9*13=18*13