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a group of friends are getting together for milk and cookies. Kramkas has ten less cookies than the cookie monster. Mr. Syph has four time more cookies then krankas. Ms. Langberg has 60 less cookies than Mr. Syph. Together they have 200 cookies. Write an equation and determine how many cookies each friend has

Sagot :

semsee45

Answer:

cookie monster = 35 cookies

Kramkas = 25 cookies

Mr Syph = 100 cookies

Ms Langberg = 40 cookies

Step-by-step explanation:

Let CM = cookie monster

Let K = Kramkas

Let S = Mr Syph

Let L = Ms Langberg

Write expressions for the info:

K = CM - 10

S = 4K

L = S - 60

Rewrite the expressions in terms of one variable (CM):

K = CM - 10

S = 4K = 4(CM - 10) = 4CM - 40

L = S - 60 = 4(CM - 10) - 60 = 4CM - 40 - 60 = 4CM - 100

  CM + K + S + L = 200

⇒ CM + (CM - 10) + (4CM - 40) + (4CM - 100) = 200

⇒ CM + CM + 4CM + 4CM = 200 + 10 + 40 + 100

⇒ 10CM = 350

⇒ CM = 35

⇒ K = CM - 10 = 35 - 10 = 25

⇒ S = 4K = 4 x 25 = 100

⇒ L = S - 60 = 100 - 60 = 40

cookie monster = 35 cookies

Kramkas = 25 cookies

Mr Syph = 100 cookies

Ms Langberg = 40 cookies

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