[gnodar]

It is hard, but only if you try to find the general solution. If instead you think in the way the problem designer (who had a target audience of 3rd graders in mind) intended the solution to be found, then it becomes easy to find a solution: one of each toy from the yo-yo to the car (inclusive). That gets you $5.18 from the goal of $43.94, so get another car (the problem doesn't state you can't have repeats).

[exporectomy]

Then it's a matter of luck whether you tried that pattern. I started with the highest prices items and didn't get far. It's mostly a lottery if it depends on people guessing that way.

I would start several approaches like writing a formula, bounding the number of toys (6 to 50?), looking for easy multiples, etc. the declare them all too hard and quit.

[bottled_poe]

Unfortunately that’s exactly the issue here. That justification puts more focus on training a (simplified and flawed) process rather than understanding the fundamental nature of the problem being presented.

[Aerroon]

But that's how you build to to the learning about the eventual general solution.

First graders here get fill in the blank questions:

__ + 3 = 10

Years later they'll learn

x + 3 = 10

Filling in the blanks isn't that hard for most kids, but dealing with x can be.

[jameshart]

The question doesn't ask you to find a solution - it says "what combinations" can you find - plural.

You're not done when you've found one. Are you sure you can't buy ten yoyos, three cars and a pinwheel and hit the number too?

[novia]

If you keep reading it asks if your solution was the only possible solution. This implies that you only have to give one solution and prove that there are no other solutions (very difficult) or find two solutions to show that there could be many more than just one.

When the son said that some people in the class got the problem exactly right, I doubt they spit out all 279 combinations.