a farmer said to another farmer , if you give me one of your horses, we'll each have the same number. the other replied, if you give me one horse, i will have twice as many as you. How many horses did each have to begin with? I know it is 5 and 7, but i do not know how to solve it algebraically

Question

nikato · Answer

Ok, let a be farmer 1 and b be 2. U can write some equations with the given info.

a+1=b-1

b+1=2a

nikato · Answer

For the first equation, add 1 to both sides so

a+2=b

nikato · Answer

Wait second equation is b+1=2(a-1)

nikato · Answer

Substitute this^ to the second equation

a+2+1=2(a-1)
Simplify

a+3=2a-2
and then a=5

nikato · Answer

Then substitute a back to one of the original to get b

nikato · Answer

Do u have any questions about this?^ @jesslovespink96

anonymous · Answer

so i substitute the second equation with the one that says simplify under it?

nikato · Answer

No, simply is just me simplifying.

U see my second post and the equation after add 1 to both sides, the one with b=a+2.

U want substitr the value of b into the second original equation

nikato · Answer

And after substitution u should get the equation above simplify

anonymous · Answer

oh yes i got the right answer, thank you very much!

nikato · Answer

Yea, no problem

whpalmer4 · Answer

Here's another version:

$$a + 1 = b - 1$$$$2(a-1) = b+1$$
Those are the two statements made between the farmers, translated to equations as before. Now we will expand the second equation and multiply each term by -1:
$$a + 1 = b - 1$$$$-2a+2 = -b - 1$$Now I add the two equations together, down the columns:
$$a - 2a + 1 + 2 = b - b - 1 - 1$$$$-a + 3 = -2$$$$a = 5$$Substitute our value of $a$ back into either of the original equations and solve for $b$:
$$5+1=b-1$$$$6=b-1$$$$7=b$$or$$2(5-1) = b+1$$$$8=b+1$$$$7=b$$

whpalmer4 · Answer

I multiplied by -1 so that when I added the equations together, the $b$ terms cancelled each other out, leaving me an equation just in terms of $a$ to solve.