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The sum of the ages of a wood plaque and a bronze plaque is 20 years. Four years ago, the bronze plaque was one-half the age of the wood plaque. Find the present age of each plaque.

Respuesta :

let age of wood plaque = x and age of the bronze one be y 
Then we have the system of equations:-

x + y = 20 ..................................(1)
y - 4 = 0.5(x - 4)
y - 0.5x = 2.................................(2)
Subtract (2) from (1):-
1.5x = 18
x = 12

from equation (1):-
12 + y = 20
y = 8

ANSWER: bronze plaque is 8 years old and wood plaque is 12 years old.



Lanuel

The present age of each plaque are 12 and 8 years respectively.

  • Let the age of the wood plaque be W.
  • Let the age of the bronze plaque be B.

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

[tex]W + B = 20[/tex]  ......equation 1

[tex]W - 4 = 2(B - 4)[/tex]   .....equation 2

[tex]W - 4 = 2B - 8\\\\W = 2B - 8 + 4\\\\W = 2B - 4[/tex]......equation 3

Substituting eqn 3 into eqn 1, we have;

[tex]2B - 4 + B = 20\\\\3B - 4 = 20\\\\3B = 20 + 4\\\\3B = 24\\\\B = \frac{24}{3}[/tex]

Bronze plaque, B = 8 years

For Wood plaque;

[tex]W = 2B - 4[/tex]

Substituting the value of B, we have;

[tex]W = 2(8) - 4\\\\W = 16 - 4[/tex]

Wood plaque, W = 12 years

Therefore, the present age of each plaque are 12 and 8 years respectively.

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