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Arada [10]
3 years ago
14

At a movie theater they sell hotdogs and popcorn. The first hour they sold 15 popcorns and 14 hotdogs for a total of $84. The se

cond hour they made $99 selling 18 popcorns and 16 hotdogs. What is the price of 1 hotdog and 1 popcorn? Can anyone help please.
Mathematics
1 answer:
Delicious77 [7]3 years ago
8 0

Answer:

1 hotdog cost $2.25

1 popcorn cost $3.5

Step-by-step explanation:

Let the price of hotdog be and that of popcorn be p

For the first hour;

15p + 14h = 84 •••• (i)

for the second hour;

18p + 16h = 99 •••••(ii)

so we want to solve these two equations simultaneously

In equation 1,

14h = 84-15p

h = (84-15p)/14

Simply insert this into equation ii

18p + 16(84-15p)/14 = 99

Multiply through by 14

252p + 1344 - 240p = 1386

1386-1344 = 252p-240p

12p = 42

p = 42/12

p = $3.5

to get cost of hotdogs;

h = (84-15p)/14

Substitute p = 3.5

h = (84-52.5)/14

h = 31.5/14

h = 2.25

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Step-by-step explanation:

7h + 4 > 5 - 5h

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5 0
3 years ago
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Add the following complex numbers: (5-3i)+(10+5i)
serious [3.7K]

Answer:

i = 7.5

Step-by-step explanation:

(5-3i)+(10+5i)

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6 0
3 years ago
What value of x will make the given triangles congruent?
Molodets [167]
Because you're trying to make them congruent, equal the two expressions to each other. 

So, for #10 you would equal them so it would look like this. 
2x+2=5x-19

Then you would just go ahead and simplify

2x+2=5x-19
-2x     -2x
---------------
2= 3x -19
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21=3x
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3     3

x=7

This means that x should be 7. You can check this just by plugging it in

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5(7)-19= 16

Same with #11.

x+8=3x-14
-x     -x
--------------
8=2x-14
+14   +14
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22=2x
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2     2

x=11

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x+8
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6 0
3 years ago
Simplify 8r - 3j + 9j - 2r
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Paul has $30,000 to invest. His intent is to earn 15% interest on his investment. He can invest part of his money at 8% interest
jeka94

Answer:

Amount invested at 8% is $9000 and amount invested at 18% is $21000.

Step-by-step explanation:

Let amount invested at 8% be x.

Let amount invested at 18% be y.

We get the 1st equation as:

x+y=30000       ........(1)

We get the second equation as:

0.08x+0.18(y)=0.15\times30000

=> 0.08x+0.18y=4500

or getting rid of the decimal by multiplying by 100 on both sides.

8x+18y=450000          ........(2)

Multiplying (1) by 8 and subtracting from (2) we get

10y=210000  

So, y = 21000

And x+21000=30000

x = 30000-21000

So, x = 9000

Therefore, amount invested at 8% is $9000 and amount invested at 18% is $21000.

6 0
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