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KengaRu [80]
3 years ago
9

S less than a quotient of a number y and 2

Mathematics
1 answer:
wel3 years ago
8 0
Xy/2-S? I think I read that properly, It should be correct.
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Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each
Basile [38]

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:

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

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so

The cookies left in each bag are

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

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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

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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

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