Answer:
ABCDE is a regular pentagon with congruent diagonals BE and BD. a) Justify AABE = ACBD with a test for congruent triangles. b) Name a pair of congruent quadrilaterals.
The present age of Madison is 1027 years and that of his mother is 3080 years (rounded off to nearest whole numbers), solved using the linear equation in one variable: (x + 614) + (3x + 614) = 5334, where x represents the present age of Madison.
Linear equations in one variable are the linear relationship between two algebraic expressions not involving more than one variable throughout the equation.
In the question, we are informed that the present age of Maison's mother is 3 times that of Madison. After 614 years, the sum of their age will be 5334 years.
We are asked to determine their present ages.
We assume the present age of Madison to be x years.
Therefore, the present age of Madison's mother = 3x years {3 times that of Madison}.
Now, after 614 years, both of their ages will increase by 614 years.
Therefore, age of Madison after 614 years = x + 614 {Present + 614}.
Age of Madison's mother = 3x + 614 {Present + 614}.
We are given that after 614 years, the sum of their ages will be 5334.
This can be represented by the linear equation in one variable:
(x + 614) + (3x + 614) = 5334
This linear equation in one variable can be simplified and solved in the following way:
or, 4x + 1228 = 5334 {Simplifying},
or, 4x + 1228 - 1228 = 5334 - 1228 {Subtracting 1228 from both sides}
or, 4x = 4106 {Simplifying}
or, 4x/4 = 4106/4 {Dividing both sides by 4},
or, x = 1026.5 {Simplifying}.
Therefore, the present age of Madison = x = 1026.5 = 1027 years (nearest whole number).
The present age of Madison's mother = 3x = 3*1026.5 = 3079.5 = 3080 years (nearest whole number).
Learn more about linear equations in one variable at
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