John and Sarah are each saving money for a car. The total amount of money John will save is given by the function f(x)= 60 + 5x. The total amount of money Sarah will save is given by the function g(x)=x^2+46. After how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

Hi,
they both amount would be same when

f(x)=g(x)

60+5x=x^2+46
x^2+46-5x=60
x^2-5x-14=0
x^2-7x+2x-14=0
(x+2)(x-7)=0

if x= weeks than x should be positive so x=7

In 7 weeks both will save same amount.

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-30T10:36:41+02:00

After 7 weeks, they both have the same amount of money saved if John and Sarah are each saving money for a car.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have

The total amount of money John will save is given by the function

f(x)= 60 + 5x

The total amount of money Sarah will save is given by the function g(x)=x²+46

To find how many weeks, x, will they have the same amount of money saved.

Equate both the functions;

f(x) = g(x)

60 + 5x = x²+46

x²- 5x—14 = 0

After solving, we get:

x = 7 or x = -2 (number of weeks cannot be negative)

So x = 7 weeks

Thus, after 7 weeks, they both have the same amount of money saved if John and Sarah are each saving money for a car.

Learn more about the function here:

brainly.com/question/5245372

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