Question

Please Help!

How do i solve this?

The product of two consecutive numbers is 14 less than 10 times the smaller number. Find each number

Answer 1

You need to write out the equation. Use x as the value of the smaller number. What would the equation look like?

Answer 2

erm

Answer 3

i have no idea

Answer 4

Let me look at this

Answer 5

The first side of the equation says the product of 2 consecutive numbers..any thoughts on what the equation for that side would look like. Remember product is multiplication.

Answer 6

1st X 2nd?

Answer 7

Close..x is the unknown and we will use x to represent the smaller number. If the number are consecutive what formula would represent the next higher number

Answer 8

10x-14?

Answer 9

We are only looking at the left side of the equation. 10x - 14 is correct for the right side of the equation. So if x = the smaller number what would represent the next higher number? (example if x=12 what would represent the next higher number?}

Answer 10

y?

Answer 11

sorry im really bad at this

Answer 12

If x = 12..the next higher consecutive number would be 13. So algebraically we would write that as x+ ?

Answer 13

x+1?

Answer 14

That is correct. When dealing with consecutive numbers x will represent the smallest number and (X+1) will represent the next highest consecutive number. Now we know that we have to multiply these x and x+1. So how would you write the equation now given you already solved the left side as 10x-14.

Answer 15

\[X \times (X+1)=10x+1\]

Answer 16

-14 i meant

Answer 17

Excellent..now if we simplify the left side...what would it look like

Answer 18

X^2+x

Answer 19

Good so our equation now looks like x^2+x=10x-14. What do you think we should do next?

Answer 20

get all the x on one side?

Answer 21

I like that idea...So what would our equation look like now?

Answer 22

Hey um i have to go eat so if you wouldnt mind posting the steps then I would be grateful

Answer 23

x^2+x = 10x-14 Subtract 10 x from both sides we get

x^2-9x = -14 Now we need to solve as a quadratic equation. If we add 14 to both sides we get

x^2-9x+14 =0 now we must factor the equation. You can use the quadratic formula

(x-7) (x-2) =0

Now solve for x...x-7=0 and x-2=0.

X=7 and X=2 If x represents the smaller value of two consecutive numbers then our answer is (7 and 8) and (2and 3)