Question

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Amelle is shopping for children's books and puzzle books. She wants to purchase at least 2 more children's books than puzzle books, but she can afford no more than 15 items total. If x represents the number of children's books and y represents the number of puzzle books Amelle purchases, which point lies in the solution set?


-BARBIE

Answer 1

Answer:

x = 9

y = 6

Step-by-step explanation:

1. Divide 15 by 2: 15 ÷ 2 = 7.5
2. Subtract 0.5 from 7.5 (this will later be added back): 7.5 - 0.5 = 7
3. Subtract 1 from 7 (she wants to buy at least 2 more children books): 7 - 1 = 6
4. Subtract 6 from 15 (6 being the number of puzzle books, 15 being the total number of items): 15 - 6 = 9 (number of children books)

Answer 2

Any ordered pair which is less than the ordered pair $(\frac{17}{2},\frac{13}{2} )$ is the answer.

Inequality Solution:

The inequality solution to the linear equation is a method to find less than or greater than value of involved variables

If x represents the number of children's book and y represents the number of puzzle books then by the given given condition,

Amelle can not afford more than 15 items.

x + y ≤ 15

Also we have given that she purchase 2 extra children's book than puzzle book that is x > y + 2

How to find the solution of inequality ?

Subtracting 2 from both the sides in second inequality

y < x-2

Substitute the value of y into first inequality

we have x + x -2 ≤ 15

2x -2  ≤ 15

2x ≤ 17

x ≤ 17/2

Now subtitute the value x into first inequality

$y < \frac{17}{2}- 2$

y < 13/2

Therefore any value which is less than $(\frac{17}{2},\frac{13}{2} )$ will lie in the solution set.

For example :$(\frac{17}{3},\frac{13}{3} )$ will lie in the solution set.

Hence any value which is less than the ordered pair $\\(\frac{17}{2},\frac{13}{2} )$ will be the answer.

This is the final answer.

Learn more about inequality solution here-https://brainly.com/question/25275758

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