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Pavel [41]
3 years ago
15

Yesterday a movie theater sold 280 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, th

e movie theater made $610 from popcorn sales. Find how many bags of each size of popcorn were sold
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
7 0

Answer:

110 large bags and 170 small bags of popcorn were sold.

Step-by-step explanation:

Since yesterday a movie theater sold 280 bags of popcorn, and a large bag of popcorn costs $ 4 while a small bag of popcorn costs $ 1 and in all, the movie theater made $ 610 from popcorn sales, to find how many bags of each size of popcorn were sold, the following calculation must be performed:

280 x 4 + 0 x 1 = 1120

140 x 4 + 140 x 1 = 700

130 x 4 + 150 x 1 = 670

110 x 4 + 170 x 1 = 610

Therefore, 110 large bags and 170 small bags of popcorn were sold.

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Answer:

x=133 y=-25

Step-by-step explanation:

I'll do both ways for you. So let's start with Substitution:

With the sub method, you have to set both equations equal to each other by setting them equal to the same variable. Since there is no coefficient in front of both x's in both equations, that variable will be easiest to solve for.

x + 2y = 83    &    x + 5y = 8

Solve for x.

x = 83 - 2y     &    x = 8 - 5y

Once you have solved for x, set each equation equal to one another and solve for y now.

83 - 2y = 8 - 5y

Isolate all variables to one side:

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Now subtract the 8 to fully isolate the y variable:

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Divide by -3:

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x + 2(-25) = 83

x - 50 = 83

x = 133

Now for the Elimination method. For this method you need to get rid of a variable by either subtracting/adding each equation together. Again, since you can subtract and x from both equations, you will be left with only the y variable to solve:

Put each equation on top of one another and subtract:

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- (x + 5y = 8)

The x's will cancel out:

(x - x) + (2y - 5y) = (83 - 8)

Simplify:

-3y = 75

Solve for y

y = -25

Then, plug y = -25 into one of the original equations:

x + 5(-25) = 8

Solve for x:

x - 125 = 8

x = 133

Hope this helps!

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