Algebra-2

To determine how many dresses of each type Sarah should buy, we can set up a system of equations based on the information given.

Step 1: Define Variables

Let:

1.( s ) = number of summer dresses

2.( w ) = number of winter dresses

3.( f ) = number of formal dresses

 

Step 2: Set Up the Equations

Based on the problem, we can create the following equations:

Total Dresses: Sarah wants to buy a total of 80 dresses.

s + w + f = 80 (Equation 1)

 

Budget: The total cost of the dresses should not exceed $2,150.

25s + 30w + 35f = 2150 (Equation 2)

 

Relationship Between Dresses: She wants to buy six times as many summer dresses as formal dresses.

s = 6f (Equation 3)

 

Step 3: Substitute Equation 3 into the Other Equations

Now we substitute Equation 3 into Equations 1 and 2.

Substituting into Equation 1:

6f + w + f = 80

7f + w = 80 (Equation 4)

 

Substituting into Equation 2:

25(6f) + 30w + 35f = 2150

150f + 30w + 35f = 2150

185f + 30w = 2150 (Equation 5)

 

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