Teaching Multiplication in 1917

[Heinz Hershold]

I could not scroll to the question either but here is my solution:
X + Y – 20 = 0.8X + 1.2Y
0.8X = 1.2 Y
Substituting for X : X = 1.5Y
1.5Y + Y – 20 = 1.2Y + 1.2 Y
0.1Y = 20 , Y = 200 , X = 300
Did the question ask for the cost of each farm? If so that is $200 and $300
If the question asked for the selling price of each farm, that is $240 each

Once the question is put into a mathematical form, the solution is easy.
The real challenge is to take the word problem and translate it into a mathematical problem. This is something that still cannot be done by a computer as it requires the ability to think. Yeah, I had to think about it (the word problem) for almost an hour. The math took 5 minutes.

[SkepticTank]

Mine took far more steps:
X = Sales price of each
A = Purchase price of A
B = Purchase price of B

X = 1.2A (20% gain)
X = .8B (20% loss)

Profit on A - Loss on B = -$20
(1.2 A - A) - (B - .8B) = -20

.2A - .2B = -20
A - B = -100
A = B - 100

Sale price - cost = -20
2X - A - B = -20
Substitute for A
2X - (B-100) -B = -20

2X - 2B = -120
X - B = -60
.8B - B = -60
-.2B = -60
B = 300
A = 200
X = 240

Here's their solution:

[Brother Daniel]

Their solution is appalling. That's no way to teach math.

[SkepticTank]

Their solution is appalling. That's no way to teach math.

It appears it was, 100 years ago.

eta: Actually, it's interesting that they title the section "arithmetic" and not "algebra". I always think of arithmetic as simple addition, subtraction, multiplication and division and Algebra as using variables (x, y, etc) to represent an unknown. They don't use any variables.

[Brother Daniel]

They do, implicitly. When they say "1% = 5/6%", they mean "1% of [some variable] = 5/6% of [some other variable]". It's horribly sloppy.

(So yeah, I guess I'm agreeing that it's interesting that they call it "arithmetic".)

[SkepticTank]

[BobCox]

From the POV prevalent it seems to have worked.