Respuesta :
I just took the test. For PLATO the first blank is 30 and the second blank is 2.
Answer:
Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]
Part 2) Jessica has at least 2 cookies more than Martha.
Explanation:
Let Jessica has x cookies.
Let Martha has y cookies.
Total cookies they have = 30
Equation forms:
[tex]x+y=30[/tex] or [tex]y = 30-x[/tex] .....(1)
Each of them ate 6 cookies from their bag.
Cookies left with Jessica = [tex]x-6[/tex]
Cookies left with Martha = [tex]y-6[/tex]
The product of the number of cookies left in each bag is not more than 80.
[tex](x-6)(y-6) \leq 80[/tex] ....(2)
Substituting [tex]y = 30-x[/tex] in equation (2)
[tex](x-6)(30-x-6) \leq 80[/tex]
=> [tex](x-6)(24-x) \leq 80[/tex]
=> [tex]24x-x^{2}-144+6x \leq 80[/tex]
=> [tex]-x^{2}+30x-144 \leq 80[/tex]
=> [tex]-x^{2}+30x-224 \leq 0[/tex]
Multiplying both sides by -1.
[tex]x^{2} -30x+224 \geq 0[/tex]
Solving this quadratic equation, we get
[tex]x\leq 14[/tex] or [tex]x\geq 16[/tex]
We will take x = 16 (bigger value as Jessica has more cookies)
And y = [tex]30-16=14[/tex]
y = 14
So, Jessica has 16 cookies.
Martha has 14 cookies.
Cookies left in the bag :
Jessica : [tex]16-6=10[/tex] cookies
Martha : [tex]14-6=8[/tex] cookies
Therefore, Jessica has at least 2 cookies more than Martha.
