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Monica [59]
3 years ago
15

Josh sold 465 bottles of apple cider and 605 bottles of wine. He made $10,050 altogether. If he sold 465 bottles of apple cider

and only 586 bottles of wine, he would just make $9,822. How much did 605 bottles of wine sell for? $______
Mathematics
2 answers:
kow [346]3 years ago
8 0

Answer:   605 bottles of wine sell for $5,445

Step-by-step explanation:

Hi, we have to write an equation for each case

465 a + 605w =10050

465a+586w=9882

Where “a” is the price of a bottle of apple cider, and “w”is the price of a bottle of wine.

Solving for a in the first equation

465 a + 605w =10050

465a =10050-605w

a= (10050-605w)/465

a= 21.61-1.30w

Replacing "a" in the second equation

465 ( 21.61-1.30w) +586w=9882

10048.65 -604.5w +586w=9882

-604.5w+586w =9882-10048.65

-18.5w=-166.65

w= -166.65/-18.5

w= 9  

Each bottle of wine sells for $9,  

605 bottles:

605x9 = $5,445

Anon25 [30]3 years ago
4 0

Answer:

465a + 605w = $10050

465a + 586w = 9822

465a + 605w = 10050

-465a - 586w = -9822

19w = 228

w= $12 each for wine

465a + 605(12)= 10050

465a + 7260= 10050

465a = 2790

a =$6 each apple cider

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Triangle ABC with vertices A(2, 4) , B(4, 0) , and C(6, 6) is dilated about the origin to be triangle A′B′C′ .
natka813 [3]

Answer:

Triangle ABC is dilated by a scale factor of 1.5

Step-by-step explanation:

The general rule for the dilation about the origin with a factor of k is

(x,y)\rightarrow (kx,ky)

You are given two triangles ABC and A'B'C'.

In triangle ABC:

  • A(2,4)
  • B(4,0)
  • C(6,6)

From the diagram, in triangle A'B'C':

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As you can see

  • A(2,4)\rightarrow A'\left(\dfrac{3}{2}\cdot 2,\ \dfrac{3}{2}\cdot 4\right)=A'(3,6)
  • B(4,0)\rightarrow B'\left(\dfrac{3}{2}\cdot 4,\ \dfrac{3}{2}\cdot 0\right)=B'(6,0)
  • C(6,6)\rightarrow C'\left(\dfrac{3}{2}\cdot 6,\ \dfrac{3}{2}\cdot 6\right)=C'(9,9)

So, triangle ABC is dilated by a scale factor of \dfrac{3}{2}=1.5

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