Essica 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 …

Question

asked Nov 27, 2019 93.2k views

2 Answers

Peter Loudon · Answer 1 · 2019-12-01T07:08:01+0000

Answer:

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.

Step-by-step explanation:

Let Jessica has x cookies.

Let Martha has y cookies.

Total cookies they have = 30

Equation forms:

x+y=30 or
y = 30-x .....(1)

Each of them ate 6 cookies from their bag.

Cookies left with Jessica =
x-6

Cookies left with Martha =
y-6

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

$(x-6)(y-6) \leq 80$ ....(2)

Substituting
y = 30-x in equation (2)

$(x-6)(30-x-6) \leq 80$

=>
$(x-6)(24-x) \leq 80$

=>
$24x-x^(2)-144+6x \leq 80$

=>
$-x^(2)+30x-144 \leq 80$

=>
$-x^(2)+30x-224 \leq 0$

Multiplying both sides by -1.

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

Solving this quadratic equation, we get

$x\leq 14$ or
$x\geq 16$

We will take x = 16 (bigger value as Jessica has more cookies)

And y =
30-16=14

y = 14

So, Jessica has 16 cookies.

Martha has 14 cookies.

Cookies left in the bag :

Jessica :
16-6=10 cookies

Martha :
14-6=8 cookies

Therefore, Jessica has at least 2 cookies more than Martha.