mager
thin
Very thin, with little body fat. Refers to people or animals.
Nach seiner langen Krankheit war er sehr mager geworden.
After his long illness, he had become very thin.

thin / lean / meager
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thin
Very thin, with little body fat. Refers to people or animals.
Nach seiner langen Krankheit war er sehr mager geworden.
After his long illness, he had become very thin.

The meaning of 'mager' depends strongly on the noun it describes. With people and animals, it means 'dünn' (thin); with foods, it means 'fettarm' (low-fat/lean); and with results or quantities, it means 'gering' (small) or 'unzureichend' (insufficient).
Der Streuner war ein magerer Hund.
The stray was a thin dog.
When 'mager' describes a person, it often has a slightly negative or concerned connotation. It usually implies that someone is underweight or unhealthily thin.
Der Arzt sagte, der Patient sei zu mager und müsse zunehmen.
The doctor said the patient was too thin and needed to gain weight.
In the context of nutrition, 'mager' is frequently combined with certain foods. Typical examples are 'mageres Fleisch' (lean meat), 'magerer Joghurt' (low-fat yogurt), 'Magerquark' (low-fat quark), or 'magere Milch' (low-fat milk).
Zum Frühstück esse ich gerne Magerquark mit Früchten.
For breakfast I like eating low-fat quark with fruit.
In its figurative meaning, 'mager' is often used for abstract things. Common combinations are 'eine magere Ernte' (a meager harvest), 'ein mageres Gehalt' (a meager salary), or 'ein mageres Ergebnis' (a meager result).
Mit einem so mageren Lohn kann man kaum eine Familie ernähren.
With such a meager wage, you can hardly support a family.
scarce / just under / close
'knapp' and 'mager' can both express that there is little of something. 'knapp' mainly says that the amount is just enough or almost not enough, for example money, time, or space. In its figurative meaning, 'mager' often sounds more negative: it means that a result, an offer, or an amount is disappointingly small. Learners may confuse the words because both can mean 'little'. As a guide: with resources like time or money, 'knapp' is very natural; with weak results or poor offers, 'mager' often fits.

Die Ausbeute auf dem Flohmarkt war mager: Ich habe nur ein altes Buch gefunden.
The haul at the flea market was meager: I found only one old book.
Vor der Reise ist das Geld knapp, deshalb buchen wir ein günstiges Zimmer.
Money is tight before the trip, so we are booking an inexpensive room.