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Alan has two more than twice as many chocolates as does alice, and half as many chocolates as does nadia. if alice has ‘a' number of chocolates, then in terms of ‘a', how many chocolates do alan, alice and nadia have

Respuesta :

anchitthawi
Alan has two more than twice as many chocolates as does alice
Alan = 2Alice + 2 ----(1)

Alan has half as many chocolates as does nadia
Alan = 1/2 Nadia
so Nadia = 2Alan ----(2)

if Alice has 'a' number of chocolates
from (1)
Alan = 2a + 2 ----(3)
from (2) and (3)
Nadia = 2 (2a+2) = 4a+4 ----(4)

So Alan Alice and Nadia have
(2a+2) + a + (4a+4) = 7a+ 6 #

This question is solved using a system of equations, which we solve symbolically as function of a.

I am going to say that:

  • Alan has x chocolates.
  • Alice has y chocolates.
  • Nadia has z chocolates.

Doing this, we get that:

  • Alan has 2a + 2 chocolates.
  • Alice has a chocolates.
  • Nadia has 4a + 4 chocolates.

Alice:

Alice has a chocolates, thus: [tex]y = a[/tex]

Alan:

  • Two more than twice as many chocolates as Alice.
  • Alice has a chocolates.

Thus:

  • Twice as many as Alice is [tex]2a[/tex]
  • Two more than twice as many is: [tex]2a + 2[/tex]

Meaning that Alan has 2a + 2 chocolates.

Nadia

  • Alan has half as many as Nadia, thus, Nadia has twice as many as Alan.
  • Alan has 2a + 2 chocolates.

Twice as Alan is: [tex]2(2a+2) = 4a + 4[/tex]

Meaning that Nadia has 4a + 4 chocolates.

A similar question is given at https://brainly.com/question/24104709

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