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At the present time, Mrs. Bee's age is six years more than four times her son's age. Three years
ago, she was seven times as old as her son was then. If (b) represents Mrs. Bee's age now and (s)
represents her son's age now, write a system of equations that could be used to model this
scenario. Use this system of equations to determine, algebraically, the ages of both Mrs. Bee
and her son now. Determine how many years from now Mrs. Bee will be three times as old as
her son will be then.

Respuesta :

cryssatemp

Answer:

Mrs. Bee current age=38 years

Son current age=8 years

In 7 years Mrs. Bee will be three times as old as  her son will be then

Step-by-step explanation:

We are told that currently Mrs. Bee's age [tex]b[/tex] is six years more than four times her son's age [tex]s[/tex]:

[tex]b=6+4s[/tex] (1)

Then, we are told that three years  ago, she was seven times as old as her son was then:

[tex]b-3=7(s-3)[/tex] (2)

At this point we ave a system of two equations with which we can find Mr. Bee's and her son's current age.

Substituting (1) in (2):

[tex]6+4s-3=7(s-3)[/tex] (3)

Finding [tex]s[/tex]:

[tex]s=8[/tex] (4) This is the son's current age

Substituting (4) in (1):

[tex]b=6+4(8)[/tex] (5)

Finding [tex]b[/tex]:

[tex]b=38[/tex] (6) This is Mrs. Bee's current age

Now we have to determine how many years [tex]x[/tex] from now Mrs. Bee will be three times as old as  her son will be then:

[tex]38+x=3(8+x)[/tex] (7)

Isolating [tex]x[/tex]:

[tex]x=7[/tex] This means that in 7 years Mrs. B will be three times as old as  her son will be then.

akposevictor

Using system of equations:

  • The age of Mrs. Bee now is: 38 years
  • The age of her son now is: 8 years
  • From now, Mrs. Bee will be 3 times as old as her son in: 7 years

First, translate the statements given into a system of algebraic equations that models the situation given.

  • b = Mrs. Bee's age now
  • s = her son's age now

Mrs. Bee's age, at present, is:

b = 4s + 6 ---> (Eqn. 1).

Three years ago, Mrs. Bee was:

b - 3 = 7(s - 3) ---> (Eqn. 2).

Solving the system of equations using the substitution method, substitute b for (4s + 6) into eqn. 2.

b - 3 = 7(s - 3) ---> (Eqn. 2).

4s + 6  - 3 = 7(s - 3)

4s + 3 = 7s - 21

  • Add like terms together

4s - 7s = -3 - 21

-3s = -24

  • Divide both sides by -3

s = 8 (her son is 8 years now)

Substitute s = 8 into eqn. 1.

b = 4s + 6 ---> (Eqn. 1).

b = 4(8) + 6

b = 38 (Mrs. Bee is 38 years now)

Let x represent the number of years from now that Mrs. Bee will be three times as old as her son.

  • Therefore:

38 + x = 3(8 + x)

  • Solve for x

38 + x = 24 + 3x

  • Combine like terms

x - 3x = 24 - 38

-2x = -14

  • Divide both sides by -2

x = 7

Thus, using system of equations:

  • The age of Mrs. Bee now is: 38 years
  • The age of her son now is: 8 years
  • From now, Mrs. Bee will be 3 times as old as her son in: 7 years

Learn more about system of equations on:

https://brainly.com/question/14202464

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