Alice, Betty and Carol all have the same amount of money (more than 50 cents but less than a dollar). Alice has two coins, Betty and Carol each have 3 coins, but Betty and Carol do not have any coins that are the same. How much money does each girl have?

Each girl has 60 cents.

Step-by-step explanation:

Since they have between 50 cents and 1 dollar, then Alice should have a 50 cent coin and 1 coin of less value (because if she had 2 coins that are worth 25 cents or less, she would have only 50 cents at most).

On the other hand, Both betty and carol need to have a coin that is at least 25 cents worth (because otherwise they would have 30 cents at most), but since they cant have the same coins, then one of them should have one 50 cent coin (and 2 small cent coins) and the other should have at least two twenty five cent coins.

Lets assume that Betty has a 50 cent coin and Carol has two 25 cent coins. Since Alice also has a 50 cent coin, then the remaining coin of Alice should have the same value than the sum of the remaining 2 coins that Betty has.

The values of the coins are 5,10, 25, 50, and 100. Since they cant have 1 dollar coins, then the only possibility for a coin to have the sum of the values of 2 coins is to have a value of 10 (10 = 5+5). Thus:

Each girl has 50+10 = 50+5+5=25+25+10 = 60 cents

72 is the answer to this problem

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: