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victus00 [196]
3 years ago
14

A father’s age is the square of his son’s age (x). In 20 years’ time the father will be 3 times as old as his son. What are the

ages of the father and son?
I am supposed to solve this by writing and solving a quadratic equation but I don't know how. The ages are 64 and 8.
Mathematics
1 answer:
VMariaS [17]3 years ago
6 0

If the current son's age is x, the current age of the father is x^2.

In 20 years they will be, respectively, x+20 and x^2+20 years old, and we know that the father will be 3 times as old as his son:

x^2+20=3(x+20) \iff x^2+20=3x+60 \iff x^2-3x-40=0

The quadratic equation has solutions

x_{1,2}=\dfrac{3\pm\sqrt{9+160}}{2}=\dfrac{3\pm 13}{2}

So, the two solutions are

x_1 = \dfrac{16}{2}=8,\quad x_2 = \dfrac{-10}{2}=-5

We clearly can't accept negative values as solution for a problem involving the age of a person, so the only feasible solution is x=8, and we deduce that the father's age is 8 squared, i.e. 64.

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4 0
3 years ago
Solve the system..???​
11Alexandr11 [23.1K]

Answer:

x = 1

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z = - 3

Step-by-step explanation:

z=-2+3x - 2y Rearrange: x + 4y3z = 18 2xy-3z9 Substitute into one of the equations:

[x+4y-3(-2+ 3x – 2y) = 18

2x-y-3(-2+3x-2y) = 9

Apply Multiplicative Distribution Law: x + 4y + 6-9x+6y=18

[2x-y+6-9x+6y=9 Rearrange unknown terms to the left side of the equation: x + 4y - 9x+6y= 18-6 2xy +6 9x+6y=9

Calculate the sum or difference:

x + 4y - 9x+6y= 12

2xy + 6-9x+6y=9

Combine like terms: -8x+10y = 12 -7x+5y+6=9 Reduce the greatest common factor on both sides of the equation: - 4x + 5y = 6 -7x + 5y + 6 = 9 Rearrange unknown terms to the left side of the equation: -4x + 5y = 6 -7x + 5y = 9-6

Subtract the two equations: -4x+5y-(-7x

+5y)= 6-(9-6)

Remove parentheses: - 4x + 5y + 7x - 5y = 6

−9+6

Cancel one variable: - 4x + 7x = 6 - 9 + 6 Combine like terms: 3x = 6 - 9 + 6

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ficient of variable: x = 3/3 Calculate the product or quotient: x = 1 Substitute into one of the equations: -4+5y = 6

Rearrange unknown terms to the left side of the equation: 5y = 6 + 4 Calculate the sum or difference: 5y = 10 Divide both sides of the equation by the coef ficient of variable: y = 10/5 Calculate the product or quotient: y = 2

The solution of the system is:

x = 1

y = 2

Substitute into one of the equations:

z = - 2 +3-2x2

Calculate the product or quotient:

z = - 2 + 3 - 4

Calculate the sum or difference:

z = 1 - 4

Calculate the sum or difference:

z = - 3 x = 1 y = 2 -3

The solution of the system is:

x = 1

y = 2

z = - 3

6 0
3 years ago
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