Serena's mom is planning her birthday party. She bought balloons, plates, and cups. Serena's mom bought twice as many plates as cups The number of balloons Serena's mom bought was half the number of cups. a. If Serena's mom bought 84 items, how many of each item did she buy? b. Tammy brought 12 balloons to the party. How many total balloons were at Serena's birthday party? c. If half the plates and all but four cups were used during the party, how many plates and cups were used?

(a)Therefore,

The number of cup = 24

The number of plate = 48

and the number of balloons =12

(b) The total number of balloons = 24

(c)The number of plates that used in party is  24

The number of cups that used in party is =20

Step-by-step explanation:

Given, Serena's mom bought balloons , plates and cups.

The number of plate was twice the number of cup.

The number of balloons was half the number of cups.

Let the number cup be x.

Since the number of plate was twice the number of cup.

The number of plate = 2x

Again the number of balloons was half the number of cups.

Then the number of balloons =

Therefore the total number of cup, plate  and balloons is

According to the problem,

⇒x=24

Therefore,

The number of cup = 24

The number of plate =(2×24)= 48

and the number of balloons =12

(b)

Given that 12 number of balloons were bought by Tammy.

Now the total number of balloons = (12+12)= 24

(c)

Given, half the plates were used in party .

The number of plates that used in party is   = 24

And all but four were used in party means that 4 cups were not used in the party.

The number of cups that used in party is = (24-4) =20

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

they will manufacture 8496 cars