Post 14: Writing Equations from Word Problems
Updated: 4 days ago
The team crossed the bridge successfully by using elimination as a solving strategy.
The passage narrows into a single stone archway, and something is already sitting in it. Not a scale, not a chasm — a sphinx, carved out of the same pale rock as the hallway, with eyes that track Sage as he approaches. It doesn't ask for numbers. It only speaks in riddles. "Answer wrong," it says, "and you'll hear this riddle again. Answer right, and I'll step aside." A few of the kids drift up behind Sage, close enough now to listen in without being asked to.
The sphinx speaks again, almost bored, like it's said this a thousand times to a thousand kids who didn't listen: "Every riddle I tell you has all the numbers you need. That was never the hard part. What trips travelers up is the order — what happens to the number first, and what happens to it after. Get the pieces right but the order wrong, and you'll hand me a perfectly sensible equation that answers a question I never asked."
Problem: Capturing the numbers, missing the relationship
"A number is decreased by five. Triple what's left, and you get twenty-one."
A) 3x − 5 = 21
B) 3(x − 5) = 21
(It's B — the decreasing happens first, so it has to happen first inside the parentheses too.)
Now watch what happens when Sage tries this on the sphinx's actual riddle: "Take a number. Triple it. Then take away seven. What's left is eleven."
Sage writes the equation like this, but something's off. Can you find it and fix it? (Click below the given line to add your correction.)
Sage grouped the subtraction inside the parentheses again — the same move that worked a second ago. But this riddle tripled the number first, and only took seven away afterward. The equation should read 3x − 7 = 11, not 3(x − 7) = 11. Solve the version Sage wrote and the answer comes out a jagged, ugly fraction. Solve the real one and it lands clean: x = 6.
A couple of the kids catch it before Sage does, muttering the riddle back and forth to each other, breaking it into pieces out loud — "triple it first, then seven comes off after, right?" — sorting out the relationship together the way they'd never have spoken in front of each other back at the number line in Post 1.
The sphinx isn't done. Try this one on your own: "Five more than twice a number is twenty-three."
Sage sets the corrected answer into the stone slot at the sphinx's feet. The creature tilts its huge head, and for a moment its carved mouth almost looks amused. Then it turns — not toward Sage, but toward the edge of the room, where the shadowy figure has been standing half in the rubble the whole time.
"Still hovering at the edges, Teddy?" the sphinx says, low, almost fond — and then it's already stepping out of the archway, like the words never happened. Sage doesn't catch the weight of it. The figure doesn't answer. But the name hangs there a second too long before the group moves on through the open passage.
The archway stays open behind them. Sage glances back at it once, unable to say why, before following the kids on into the next room.
Catch your algebra mistakes before they cost you
The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.
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