How many cupcakes does each one of them decorate?

Question

Rachael, Denzel and Thomas have a cupcake decorating party. Rachel decorates eight fewer cupcakes than Tomas, while Denzel decorates twice as many cupcakes as Rachel. In total, they decorate 60 cupcakes

Answer 1

Hi Jahroy,

Let's use the variable T to represent the number of cupcakes for Thomas.

Then we can write the following expression to represent the number Rachael decorated: T - 8

We can represent the number decorated by Denzel as : 2(T - 8)

Since the sum for all three people is 60 , we can write and solve the following equation for Thomas first and then determine the number of cupcakes for Rachael and Denzel.

Number of cupcakes for Thomas + Number of cupcakes for Rachael + Number of cupcakes for Denzel = 60

T + T - 8 + 2(T - 8) = 60

Now use the distributive property , combining like terms, and inverse operations to determine the value of T:

T + T - 8 + 2T - 16 = 60

4T - 24 = 60

4T - 24 + 24 =60 + 24

4T = 84

4T /4 = 84/4

T = 21

Thomas decorated 21 cupcakes.

Rachael would have decorated T - 8 = 21 - 8 = 13 cupcakes

Denzel would have decorated 2(T - 8) = 2 (21-8) = 2 (13) = 26 cupcakes