A mathematics workbook for elementary school children (4th grade in the United States) poses the following word problem and asks the reader to pick from 20 different toys, each with a specific price, and find combination(s) that would allow a person to spend all of the money they have ($43.94).
I am wondering if there is a straightforward way for these young students without a background in combinatorics and/or linear algebra to go about solving this problem. A trial-and-error approach may be the only viable option for them, but it seems like a rather daunting task.
My guess was wrong. One solution is to buy two tractors, four racecars and four pinwheels: $$2 \times 5.97 = 11.94\\4 \times (7.13 + 0.87) = 32.00\\32.00 + 11.94 = 43.94$$
Found by noting that tractors fall $3$ cents short of a full number of dollars, meaning two of them are needed to obtain the needed $94$ cents. Which left $\$32$. Then noticing that a racecar and pinwheel together are $\$8$.
I am doubtful it is the only solution.