Question

Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.

How many more cookies will Jessica have Martha?
If x represents the number of cookies Jessica started with, complete the statements below.

The inequality that describes the relationship between the number of cookies each one of them has is x^2 - ____ x +224 >= 0.
Jessica has at least ____ cookies more than Martha.​

Answer 1

part 1- 30

part 2- 2

To simplify it at least those are the answers

Answer 2

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is
`x^(2) -30x+224\geq 0`

Part 2) Jessica has at least 2 cookies more than Martha

Explanation:

Part 1) Find the inequality that describes the relationship between the number of cookies each one of them has

Let

x----> the number of cookies when Jessica started

30-x ----> the number of cookies when Martha started

we know that

Each of them ate 6 cookies from their bag

so

The cookies left in each bag are

(x-6) ----> Jessica

and (30-x-6)=(24-x) ---> Martha

The product is equal to (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

so

`(x-6)(24-x)\leq 80\\ \\24x-x^(2)-144+6x\leq 80\\ \\-x^(2) +30x-144-80\leq 0\\ \\-x^(2) +30x-224\leq 0`

Multiply by -1 both sides

`x^(2) -30x+224\geq 0`

Part 2) Solve the quadratic equation

`x^(2) -30x+224\geq 0`

Solve by graphing

The solution is x=16 cookies

so

(30-x)=30-16=14 cookies

therefore

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

The number of cookies left in each bag is equal to

Jessica

16-6=10 cookies

Martha

14-6=8 cookies

Jessica has at least 2 cookies more than Martha