2. Mr. Andrew wants to give each of his students an equal number of the crayons he bought. There are 32 students in Mr. Andrew’s class. How many crayons will each student get? Estimate first.

Solve the problem and explain your answer using pictures, diagrams, equations, and/or words.

3. How many more boxes of crayons does Mr. Andrew need if he wants each of his students to get 12 crayons? Explain your answer.

Step-by-step explanation:

2.

Because we don't know how many crayons he bought we will call it c.

c = total number of crayons purchased

T = total number of crayons each student gets

To determine how many crayons each student gets we divide c by 32, because that's the number of students in his class.

c / 32 = T

So let's say he purchased 120 crayons.

c = 120

120/32 = T

T = 3.75

Since he can't give a fraction of a crayon, in this case, each student will get 3 crayons.

3.

We will now pretend there are 24 crayons in 1 box.

So T still equals the total number of crayons each student gets and c still equals number of crayons purchased, but now we also have b which equals the number of crayons in 1 box.

c = total number of crayons purchased

T = total number of crayons each student gets

b = number of crayons in 1 box

x = number of boxes purchased

So b*x = c

We can still write the equation:

c / 32 = T

We know T = 12 So we plug 12 in for T

c / 32 = 12  Now multiply each side by 32, so 32 will cancel on the left.

32c/32 = 12 * 32

c = 12 * 32

c = 384

So if he needs to purchase 384 crayons we can use our other equation.

b*x = c    

b = 24

c = 384

So we plug those in.

24x = 384  Divide each side by 24 so 24 will cancel on the left.

24x/24 = 384/24

x = 384/24

x = 16

So he needs to buy 16 boxes of crayons in this instance. We can figure out how many boxes he bought in #2 by using the same equation.

b*x = c  

c = 120 in #2

b =24

24 * x = 120

24x/24 = 120/24

x = 120/24

x = 5

So for each student to have 12 crayons he needs to purchase 11 more boxes (16 - 5 = 11).

This will work for whatever numbers you were given.

Remember:

c = total number of crayons purchased

T = total number of crayons each student gets

b = number of crayons in 1 box

x = number of boxes purchased

b*x = c

c / 32 = T

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

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: