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Graphing Inequalities in Two Variables Worksheet - Page 2

Graphing Inequalities in Two Variables Worksheet
  • Page 2
 11.  
Determine whether the ordered pair (5, 20) is a solution of the inequality y < x2 + x - 10.
a.
Yes
b.
No


Solution:

y < x2 + x - 10
[Write original inequality.]

20 < 52 + 5 - 10
[Substitute 5 for x and 20 for y.]

20 < 25 + 5 - 10
[Evaluate the exponent.]

20 < 20
[Simplify.]

20 is not less than 20.

The ordered pair (5, 20) is not a solution to the inequality y < x2 + x - 10.


Correct answer : (2)
 12.  
David can afford to buy 15 mangoes and 20 oranges. He wants at least 10 mangoes and at least 10 oranges. If x represent the number of mangoes ,y represent the number of oranges that David buy , then which of the following systems of inequalities models this situation?
a.
x ≥ 15, y ≥20, x ≥ 10, y ≥ 10
b.
x ≤ 15, y ≥20, x ≥ 10, y ≥ 10
c.
x ≤ 15, y ≤20, x ≥ 10, y ≤ 10
d.
x ≤ 15, y ≤ 20, x ≥ 10, y ≥ 10


Solution:

x represents the number of mangoes bought and y represents the number of oranges that David buy

The maximum number of mangoes that can be bought is 15. So x ≤ 15.

The maximum number of oranges that can be bought is 20. So y ≤ 20.

The minimum number of mangoes to be bought is 10. So x ≥10.

The minimum number of oranges to be bought is 10. So y ≥ 10.

So, the system of inequalities that models the given situation is:
x ≤ 15, y ≤ 20, x ≥ 10, y ≥ 10.


Correct answer : (4)
 13.  
If the cost of a tape is $10 and the cost of a CD is $12, then write the objective function for the cost of x tapes and y CDs .
a.
C = 12x + 10y
b.
C = 22 + x + y
c.
C = 10x + 12y
d.
C = 120xy


Solution:

The cost of each tape is $10 and the cost of each CD is $12.

The cost C of x tapes and y CDs is C = 10x + 12y, which is the objective function for the cost.


Correct answer : (3)

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