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?

Answer:(a)Therefore,The number of cup = 24The number of plate = 48and the number of balloons =12(b) The total number of balloons = 24(c)The number of plates that used in party is  24The number of cups that used in party is =20Step-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 = 2xAgain the number of balloons was half the number of cups.Then the number of balloons =[tex]\frac{x}{2}[/tex]Therefore the total number of cup, plate  and balloons is [tex]=x+2x+\frac{x}{2}[/tex][tex]=\frac{2x+4x+x}{2}[/tex][tex]=\frac{7x}{2}[/tex]According to the problem,[tex]\frac{7x}{2}=84[/tex][tex]\Rightarrow x=\frac{84 \times 2}{7}[/tex]⇒x=24Therefore,The number of cup = 24The number of plate =(2×24)= 48and the number of balloons [tex]=\frac{24}{2}[/tex] =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  [tex]=\frac{48}{2}[/tex] = 24And 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