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Vinvika [58]
2 years ago
14

Mackenzie and her children went into a movie theater and she bought $99.50 worth of bags of popcorn and candies. Each bag of pop

corn costs $8.50 and each candy costs $4. She bought a total of 17 bags of popcorn and candies altogether. Write a system of equations that could be used to determine the number of bags of popcorn and the number of candies that Mackenzie bought. Define the variables that you use to write the system.
Mathematics
1 answer:
olga_2 [115]2 years ago
5 0

Answer: Mackenzie bought 7 bags of popcorn and 10 candies.

Step-by-step explanation:

Let x represent the number of bags of popcorn that Mackenzie bought.

Let y represent the number of candies that Mackenzie bought.

She bought a total of 17 bags of popcorn and candies altogether. This means that

x + y = 17

She bought $99.50 worth of bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs $4. This means that

8.5x + 4y = 99.5- - - - - - - - - - - - - - 1

Substituting x = 17 - y into equation 1, it becomes

8.5(17 - y) + 4y = 99.5

144.5 - 8.5y + 4y = 99.5

- 8.5y + 4y = 99.5 - 144.5

- 4.5y = - 45

y = - 45/ - 4.5

y = 10

x = 17 - y = 17 - 10

x = 7

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Veseljchak [2.6K]

Answer:

For a = 1.22 there is one solution where y = 1.3

Step-by-step explanation:

Hi there!

Let´s write the system of equations:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

-1.2(x-0.5) = 0

Let´s solve the second equation for x:

-1.2(x-0.5) = 0

x- 0.5 = 0

x = 0.5

Now let´s repalce x = 0.5 and y = 1.3 in the first equation and solve it for a:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

a(0.3 - 1.3) + 1.1 + 2.4(0.5)(1.3 -1.2) = 0

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a = 1.22

Let´s check the solution and solve the system of equations with a = 1.22. Let´s solve the first equation for y:

1.22(0.3 - y) + 1.1 +2.4(0.5)(y-1.2) = 0

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y = 1.3

Then, the answer is correct.

Have a nice day!

4 0
2 years ago
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marishachu [46]

Answer:

A )  The Equation of the circle (x−10)2+(y−24)2=676

Step-by-step explanation:

step1:-

The equation of the circle whose center is (a,b) and radius r is

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in this circle equation centre is (g,f) = (10,24)

and formula of radius of a circle is

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Step2:-

The Equation of the circle (x−10)^2+(y−24)^2=676

5 0
2 years ago
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