Question

The sum of two integers is 15. Eight times the smaller integer is one less than three times the lager integer. Find the integers.

This problem should not use system of equations. I see how to set the problem up using system of equations. How do you set the problem up using one equation similar to a consecutive equation?

Answer 1

Let's do this step by step!
X+Y=15
8X=3Y-1

Now using the second equation I want you to solve for x, okay?

Answer 2

if one integer is x, the other integer is 15-x

Answer 3

@MDoodler

Answer 4

You don't know which integer is larger, so you can arbitrarily say that either one is the "larger" or "smaller" integer. I'll take \(x\) as the larger one.

Eight times the smaller integer = 8*(15-x)
1 less than 3 times the larger integer = 3*x -1

set those two equal to each other and solve.

Answer 5

try it both ways to convince yourself that it doesn't matter whether you use x or 15-x to represent the larger integer.

Answer 6

ConDawg I can solve the problem but in my post I said not using system of equations. And having a hard time getting it to click as a consecutive problem.

whpalmer4 out of that word problem where did you get 8(15 -1)

Answer 7

well, the sum of the two is 15, right? so if we say one of them is x, the other one is 15-x, right?

Answer 8

then I arbitrarily chose \(x\) as the larger one (so \((15-x)\) is the smaller one) and set up the problem.

Answer 9

One sec

Answer 10

whpalmer4 you are saying it should be set up like 8(15-x) = 3x -1 ?

Answer 11

I thought I said that pretty clearly when I said "set those two equal to each other", but yes, that's right.

Answer 12

Yepper that is it

Answer 13

you could equally well do 8x = 3(15-x) - 1

the only difference would be that x would now be the smaller number, and you'd have to find the larger via 15-x...

Answer 14

essentially this is just collapsing the substitution step into the writing the equations step...

Answer 15

Thank you

Answer 16

What I was missing and was not thinking about was (15-x) it makes since too lol

Answer 17

some people think that writing the equations this way (instead of doing a system) is easier to understand. well, maybe it is, maybe it isn't, but I think it might be a little easier to spot mistakes the way, and I'm generally in favor of idiot-proofing my work, because it is often done by an idiot :-)

Answer 18

Well, when I read it I picked right up on it as being a system and solved it but the book I got it from was not using system of equations and I was trying to figure out how they were going about doing it. I had everything but I was missing (15 -x).

Answer 19

Thanks again.