Enter numbers in the circles so that the numbers on each line equal the sum of the numbers at each end.

The correct answers are:

Top circle: 34

Bottom left: 9

Bottom right: 21

Explanation:

Let the top circle be x, let the bottom left circle be y, and the bottom right circle be z.

Following the diagram, we have the following equaitons:

x+y = 43

y+z = 30

x+z = 55

Taking the first two equations as a system, we will eliminate y:

We will subtract the bottom equation from the top:

We will now take this and the last equation as a system; this time, we will eliminate z by adding the two equations:

Divide each side by 2:

2x/2 = 68/2

x = 34

Substitute this into the first equation:

x+y = 43

34+y = 43

Subtract 34 from each side:

34+y-34 = 43-34

y = 9

Substitute this into the second equation:

y+z = 30

9+z = 30

Subtract 9 from each side:

9+z-9 = 30-9

z = 21

Final answer:

To solve this problem, assign numbers to the circles in a way that the sum of the numbers on each line is equal at both ends.

Explanation:

This question falls under the subject of Mathematics and is suitable for a Middle School grade level. To solve it, you need to find numbers for each circle such that the sum of the numbers on each line equals the sum of the numbers at each end. Let's label the circles as A, B, C, and D. The sum of A and C must equal the sum of B and D. By assigning a value to one circle, you can find the values of the other circles. For example, if A is 3, then C must be 1, and B must be 4 since B + D must equal A + C. From there, you can continue assigning values to the rest of the circles by ensuring the sums at each end are equal.

Learn more about Mathematics here:

brainly.com/question/26854035

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