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ankoles [38]
2 years ago
10

Miss Goh bought 6 blouses, 2 skirts and 2 dresses for $560. A blouse and a skirt cost $107. A blouse and a dress cost $134. What

was the cost of a dress?
Mathematics
1 answer:
Yuri [45]2 years ago
5 0

Answer:

$95 FOR A DRESS

Step-by-step explanation:

Let's rearrange the given:

  She bought a blouse and skirt for two, a blouse and a dress for two, and a blouse for two.

     A blouse and a skirt cost $107

     A blouse and a dress cost $134

     blouse cost x dollars

The equation:

     2($107) + 2($134) + 2x = $560

SOLUTION:

   $214 + $268 + 2x = $560

   2x = $560 - $214 - $268

   2x = $78

   x = $39 for a single blouse

FIND THE COST OF DRESS:

   A blouse and a dress cost $134 - $39 for a single blouse

      $134 - $39 = $95

$95 IS THE COST OF DRESS

   

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The sides of a triangle are x , x +1 , 2 x -1 and its area is x root of 10 .Find the value of x.
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Ok, I'm going to start off saying there is probably an easier way of doing this that's right in front of my face, but I can't see it so I'm going to use Heron's formula, which is A=√[s(s-a)(s-b)(s-c)] where A is the area, s is the semiperimeter (half of the perimeter), and a, b, and c are the side lengths.

Substitute the known values into the formula:

x√10=√{[(x+x+1+2x-1)/2][({x+x+1+2x-1}/2)-x][({x+x+1+2x-1}/2)-(x+1)][({x+x+1+2x-1}/2)-(2x-1)]}

Simplify:

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<span>x√10=√[2x(2x-x)(2x-x-1)(2x-2x+1)]</span>

<span>x√10=√[2x(x)(x-1)(1)]</span>

<span>x√10=√[2x²(x-1)]</span>

<span>x√10=√(2x³-2x²)</span>

<span>10x²=2x³-2x²</span>

<span>2x³-12x²=0</span>

<span>2x²(x-6)=0</span>

<span>2x²=0 or x-6=0</span>

<span>x=0 or x=6</span>

<span>Therefore, x=6 (you can't have a length of 0).</span>

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