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balandron [24]
2 years ago
13

Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 m

agazines, he would have run short of $4.
A student concluded that the price of each CD is $5 and the price of each magazine is $6. Which statement best justifies whether the student's conclusion is correct or incorrect?
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (9, 4).
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (5, 6).
Mathematics
1 answer:
Leni [432]2 years ago
3 0
You can set up two equations from the information given. I will set them up for you:

32 = 4x + 2y
36 = 5x + 2y

Let's solve the first equation to come up with a value for y.

32 = 4x + 2y
32 - 4x = 2y
16 - 2x = y

Now we plug y into the other equation.

36 = 5x + 2(16-2x)
36 = 5x + 32 - 4x
4 = x

Now we have our real x value and we can plug it into the first equation.

32 = 4(4) + 2y
32 = 16 + 2y
16 = 2y
8 = y

Since x = 4 and y = 8, you get the final coordinates of (4,8).

Your answer is the second statement provided above.
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Answer: 12 students

Step-by-step explanation:

Let X and Y stand for the number of students in each respective class.

We know:

X/Y = 2/5, and

Y = X+24

We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:

(Y-x)/(X+x) = 1

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We can rearrange X/Y = 2/5 to:

X = 2Y/5

The use this value of X in the second equation:

Y = X+24

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5Y = 2Y + 120

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Y = 40

Since Y = X+24

40 = X + 24

X = 16

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Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:

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(40-x)=(16+x)

24 = 2x

x = 12

12 students must transfer to the more difficult, very early morning, class.

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Median

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