It seems like an age-old problem -- kids not eating their vegetables -- and it is. Little ones, more interested in macaroni and cheese than sauteed spinach, are still leaving the latter largely untouched. The proof is both anecdotal -- what parent hasn't tussled with this? -- and borne out in data. Nine out of 10 children, after all, still don't eat enough vegetables, according to the Centers for Disease Control and Prevention (CDC).

The problem has been blamed, at least in part, for the deteriorating diets of American youth. It has also been on clear display ever since the government updated, in 2013, its nutrition standards for the National School Lunch Program. Children, suddenly confronted with vegetables on every plate (as required as part of the change), have responded not by eating them but by leaving them on their plates -- untouched.

It's a poignant example of how kids are really good at making really bad decisions about food. And it has proved pretty frustrating for health and nutrition advocates, who can't seem to find a reasonable way to get children to eat more healthfully at school.

But it turns out there might be an ingenious solution hiding beneath everyone's nose.

Researchers at Texas A&M University, looking for patterns in food consumption among elementary school children, found an interesting quirk about when and why kids chose to eat their vegetables. After analyzing plate waste data from nearly 8,500 students, it seems there's at least one variable that tends to affect whether kids eat their broccoli, spinach or green beans more than anything: what else is on the plate.

Kids, in short, are much more likely to eat their vegetable portion when it's paired with a food that isn't so delicious it gets all the attention. When chicken nuggets and burgers, the most popular items among schoolchildren, are on the menu, for instance, vegetable waste tends to rise significantly. When other, less beloved foods, like deli sliders or baked potatoes, are served, the opposite seems to happen.

"Pairings of entrees and vegetables are an important consideration when assessing plate waste among elementary school children," the researchers note.

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Indeed, the effect can work the other way around. The study found that children tend to eat less of their entree when popular vegetables (mostly starchy fried vegetables, like Tater Tots and French fries, which many wouldn't classify as vegetables) are offered. When the entree is paired with steamed broccoli -- the vegetable children eat the least of on average -- kids instead eat more of the main dish.

And that interrelationship can be useful in reducing the amount of food wasted at schools, which has been a persistent problem.

But these observations are likely more useful as a gauge for how appetizing vegetable are in different contexts than as a subscription for what pairings will lead to the least amount of food waste. Kids' favorite meals, after all, aren't particularly healthful. What's more, they, too, lead to considerable waste. The most popular pairing -- hamburger and Tater Tots -- still results in about 26 percent waste on average, according to the study.

The notion that food pairings can significantly affect the attractiveness of certain foods isn't new. Traci Mann, who teaches psychology at the University of Minnesota and has been studying eating habits, self-control and dieting for more than 20 years, believes that it can, in fact, be crucial. One of the simplest ways to eat better is to make it easier to eat better. That involves a strategy Mann calls "get alone with a vegetable," which is similar in that it shows how important context can be. She described the strategy earlier this year: "Normally, vegetables will lose the competition that they're in -- the competition with all the other delicious food on your plate. Vegetables might not lose that battle for everyone, but they do for most of us." She also noted that it's been effective with kids: "We've actually tested this in a lot of ways. And it works unbelievably well. We tested it with kids in school cafeterias, where it more than quadrupled the amount of vegetables eaten.

"It's just about making it a little harder to make the wrong choices, and a little easier to make the right ones." Of course, convincing schools to serve vegetables by themselves could be too tall a task. Asking them never to serve foods kids adore might be, too. But understanding how something as simple as what a vegetable is served with can have a sizable impact on whether a child eats it is a pretty useful thing. At school, and at home.