Question

Alice has seven times the amount of pens that Maurice has. Paul has two-thirds of the amount of pens as Alice and Suzy have combined. Dawn has a dozen more pens than Paul. Suzy has half the pens that Maurice has. If Suzy has 2 pens, how many does Dawn have?

Answer 1

Answer:

Dawn has 32 pens.

Step-by-step explanation:

• Let No. of pens Alice has = A
• Let No. of pens Maurice has = M
• Let no of pens Paul has = P
• Let no. of pens Suzy has = S
• Let no of pens Dawn has = D

Given :

• A = 7M
• P = 2/3 (A + S)  
• D = P + 12
• S = 1/2 M

• If S = 2 {Given}
• M = 4    [∵ S = 1/2 M → M = 2S = 2X(2) ]
• A = 28  [ ∵ A = 7M → A = 7 x 4 ]
• P = 20  [∵ P = 2/3 (A+S) → P = 2/3 (28 + 2) = 2/3 (30) ]
• D = 32  [ ∵ D = P + 12 → D = 20 + 12 ]

Answer 2

Dawn has 32 pens which is a dozen more pens than Paul.

Let x represent the amount of pen that Alice has, y that of Maurice, z that of Paul, a that of Suzy

x = 7y

z = 2(a + x)/3

a = y/2

a = 2

a = y/2

2 = y/2

y = 4

x = 7y = 7(4) = 28

z = 2(a + x)/3 = 2(2 + 28)/3 = 20

The amount of pen Dawn has = 12 + z = 12 + 20 = 32

Therefore Dawn has 32 pens

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