MATH SOLVE

2 months ago

Q:
# 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.β

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A:

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 MarthaStep-by-step explanation:Part 1) Find the inequality that describes the relationship between the number of cookies each one of them hasLetx----> the number of cookies when Jessica started 30-x ----> the number of cookies when Martha started we know thatEach of them ate 6 cookies from their bagsoThe cookies left in each bag are(x-6) Β ----> Jessicaand (30-x-6)=(24-x) ---> MarthaThe 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[tex](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[/tex]Multiply by -1 both sides[tex]x^{2} -30x+224\geq 0[/tex]Part 2) Solve the quadratic equation[tex]x^{2} -30x+224\geq 0[/tex]Solve by graphingThe solution is x=16 cookiesso(30-x)=30-16=14 cookiesthereforeThe number of cookies when Jessica started was 16 cookiesThe number of cookies when Martha started was 14 cookiesThe number of cookies left in each bag Β is equal toJessica16-6=10 cookiesMartha14-6=8 cookiesJessica has at least 2 cookies more than Martha