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Maslowich
3 years ago
6

Mary has a pink dress, a blue dress, and a yellow dress. She has a black pair of shoes and a white pair. How many dress and shoe

outfits can she make?
Mathematics
1 answer:
Yanka [14]3 years ago
8 0
There are two ways to solve this. 
The first way is logically. 
Mary can 
-wear a pink dress with black shoes   -wear a pink dress with white shoes
-wear a blue dress with black shoes   -wear a blue dress with white shoes
-wear a yellow dress with black shoes   - wear a yellow dress with white shoes

Count them up, and you'll get six combinations! 

Another way is simply mathematically, which is easier in my opinion. 

3 (different colored dresses) × 2 (different colored shoes) = 6 (combos)
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Part A: The solution is (-0.923,5.692)

Part B: The point (3,7) is not in the solution set.

Explanation:

Part A: The given inequalities are 3 x+4 y>20 and x

The solution can be determined by solving the two inequalities by substitution method.

Changing inequalities to equality, we have,

x=3 y-18 and 3 x+4 y=20

Let us substitute x=3 y-18 in the equation 3 x+4 y=20 , we get,

3 (3y-18)+4 y=20

   9y-54+4y=20

                  13y=74

                     y=5.692

Substituting y=5.692 in x=3 y-18, we get,

x=3 (5.692)-18

  =17.076-18

x=-0.923

Thus, the solution set is (-0.923,5.692)

Part B: Now, we shall determine whether the point (3,7) is in the solution set.

Let us substitute the point (3,7) in the inequalities 3 x+4 y>20 and x, we get,

3 (3)+4 (7)>20

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            37>20

Also, substituting (3,7) in x, we get,

3

3

3

Since, the point (3,7) does not satisfy one of the inequality x , the solution set does not contain the point (3,7)

Thus, the point (3,7) is not in the solution set.

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