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three friends are comparing the ages of baseball cards they each have. Tim's card is three times as old as Tom's card. Sam's is nine more than twice more than twice as old as Tom's if the total ages of the cards is 75, how old is each friend's card?

Respuesta :

Lanuel

The ages of each friend's card are 6.6 years, 19.8 years, and 48.6 years respectively.

  • Let the age of Tim's card be T.
  • Let the age of Tom's card be O.
  • Let the age of Sam's card be S.

Given the following data:

  • Total age = 75

To determine how old is each friend's card:

Translating the word problem into an algebraic expression, we have;

For Tim's card:

[tex]T=3O[/tex]   ....equation 1.

For Sam's card:

[tex]S=2T+9[/tex]    ....equation 2.

For the total age:

[tex]T+O+S=75[/tex]    ....equation 3.

Substituting eqn. 1 into eqn. 2, we have:

[tex]S=2(3O)+9\\\\S=6O+9[/tex]...equation 4.

Substituting both eqn. 1 and eqn. 4 into eqn. 3, we have:

[tex]3O+ O+6O+9=75\\\\10O+9=75\\\\10O=75-9\\\\10O=66\\\\O=\frac{66}{10}[/tex]

O = 6.6 years.

For Tim's card:

[tex]T=3O\\\\T=3(6.6)[/tex]

T = 19.8 years.

For Sam's card:

[tex]S=2T+9\\\\S=2(19.8)+9\\\\S=39.6+9[/tex]

S = 48.6 years.

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