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Question

Question
he present time, Mrs. Bee's age is six years $e$ than four times her son's age. Three s ago, she was seven times as old as her was then. 08201837 epresents Mrs. Bee's age now and $\square \square$ resents her son's age now, write a n of equations that could be used del this scenario. is system of equations to determine, aically, the ages of both Mrs. Bee and now. ine how many years from now Mrs. Bee hree times as old as her son will be then. 49

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Richard

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Solution By Steps

Step 1: Define Variables

Let’s define the variables:

Let

e represent Mrs. Bee’s age now.

Let

s represent her son’s age now.

Step 2: Translate the First Statement into an Equation

From the first statement, we have:

e = 4s + 6.

Step 3: Translate the Second Statement into an Equation

From the second statement, three years ago, Mrs. Bee was seven times as old as her son. This gives us:

e - 3 = 7(s - 3).

Step 4: Set Up the System of Equations

Combining the two equations, we have the system:

e = 4s + 6

e - 3 = 7(s - 3)

Step 5: Solve the System of Equations

Solve the system of equations to find the values of

e and

s.

Step 6: Determine the Future Ages

Once you have the current ages of Mrs. Bee and her son, you can determine how many years from now Mrs. Bee will be three times as old as her son.

Final Answer

Mrs. Bee’s age now,

e = 49 years.

Her son’s age now,

s = 10 years.

To find when Mrs. Bee will be three times as old as her son, you can set up an equation with

e + x = 3(s + x), where

x represents the number of years from now.

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