The meaning of a math problem

Question

The math problem shows bellow,

A $\$550$ donation to community fund is to be divided among three organizations. The hospital is to get twice as much as the community recreation center and three times as much as the volunteer fire company. How much of the donation is to go to the community recreation center?

So I assume hospital donation is $H$, center donation is $C$, volunteer fire com is $V$. According to this sentence,

The hospital is to get twice as much as the community recreation center and three times as much as the volunteer fire company.

So the formula is $H＝2C＋3V$. But actually it is supposed to be $H＝2C$ or $H＝3V$.

Is it wrong for me to see the word and as plus sign? Thank you.

Answer 1

There is some precedent for using and to mean plus when sums are written out:

and conjunction 1.6 Used to connect two numbers to indicate that they are being added together. ‘six and four makes ten’ - ODO

However, the sentence can also be parsed as a form of ellipsis:

• The hospital is to get twice as much as the community recreation center and (the hospital is to get) three times as much as the volunteer fire company.

and conjunction 1 Used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly. ‘She started out quietly and apologetically but her voice quickly gained firmness.’ - ODO

Both parts of the conjunction are comparisons of the form x times as much as y.

So both interpretations can be admitted. When there's ambiguity in the sentence, it can help to look at the context and the conventions governing that context. In your case, the context is that of simple maths problems presented in written form for translation to numeric form and subjected to further analysis. In such problems, my recollection is that the word and is usually used in the sense of providing more information, rather than add up a sum.

Nevertheless, maths problems can be open to obtuse interpretations, so using conventions to disambiguate can potentially backfire. The pragmatic advice is to state your assumptions - in this case, that you take and to mean plus or, more conventionally, that the amount the hospital gets is the same as each of the two parts separately, not added together.

Answer 2

It is wrong. The word and is never used to mean plus in mathematics, although it is used like this in everyday English, e.g. "Two and two equals four." In mathematics, it is always "Two plus two equals four."

The sentence should be interpreted as:

The amount that the hospital receives is twice as much as the community recreation center receives, and also three times as much as the volunteer fire company receives (but not the sum of these two amounts).

Your summary is also incorrect. It should be:

H = 2C and H = 3V

Both equalities are true (at the same time), not one or the other.