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Anettt [7]
3 years ago
9

Three years hence a father will four times as old as his son will be. Before two years he was seven times as old as his son was.

Find their present ages.
Mathematics
2 answers:
myrzilka [38]3 years ago
7 0

Answer: The father is 37 years and the son is 7 years

Step-by-step explanation:

Let x represent the present age of the father.

Let y represent the present age of the son.

Three years hence a father will four times as old as his son will be. This means that

x + 3 = 4(y + 3)

x + 3 = 4y + 12

x - 4y = 12 - 3

x - 4y = 9- - - - - - - - - - - - - - - -1

Before two years he was seven times as old as his son was. This means that

(x - 2) = 7(y - 2)

x - 2 = 7y - 14

x - 7y = - 14 + 2

x - 7y = - 12- - - - - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

3y = 21

y = 21.3 = 7

Substituting y = 7 into equation 1, it becomes

x - 4 × 7 = 9

x - 28 = 9

x = 9 + 28

x = 37

andrey2020 [161]3 years ago
5 0

Answer:

Father 9 years

son 1 year

Step-by-step explanation:

knowing that the father is X and the son is Y we have the equation

X+3=4Y

X-2=7Y

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Answer:

2(x-3)(x-1)

Step-by-step explanation:

2(x+x+3)

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8 0
3 years ago
Read 2 more answers
Y=x^2+12x+35 into the form y=(x-h)^2+k
LiRa [457]

Answer:

y = (x + 6)² - 1

Step-by-step explanation:

So there are two ways of doing it, completing the square or partial factoring (which is what i prefer and will show)

so we will get x first:

x^2+12x

We are factoring x

x(x+12)

Now you do x=-12/2

x=-6

Now that you have x, you plg that back into the equation to get y

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4 0
2 years ago
Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid pa
enyata [817]

Answer:

Solid paper costs 1.75 each

Printed paper costs 2.50 each

Step-by-step explanation:

Given:

Ben = $43.50 (12 rolls solid paper and 9 rolls of printed paper)

Joel = $51.50 (8 rolls solid paper and 15 rolls of printed paper)

Let x = solid paper

Let y = printed paper

12x + 9y = 43.50

 8x + 15y = 51.50

Find x:

8x + 15y = 51.50

8x = 51.50 - 15y

x = (51.50 - 15y)/8

Substitute x:

12x + 9y = 43.50

12(51.50 - 15y)/8 + 9y = 43.50

(618 - 180y)/8 + 9y = 43.50

8 (618 - 180y)/8 + 8*9y = 43.50 * 8

618 - 180y + 72y = 348

-108y = 348 - 618

-108y = -270

-108y/-108 = -270/-108

y = 2.50

x = (51.50 - 15y)/8

x = (51.50 - 15(2.5) /8

x = (51.50 - 37.50)/8

x = 14/8

x = 1.75

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12x + 9y = 43.50

12(1.75) + 9(2.5) = 43.50

21 + 22.50 = 43.50

43.50 = 43.50

8x + 15y = 51.50

8(1.75) + 15(2.5) = 51.50

14 + 37.50 = 51.50

51.50 = 51.50

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Step-by-step explanation:

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