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

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. ;

Answered by NetaLeeHershlag | 2024-06-18

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:
{ z + y = 30 x + y = 43 ​
We will subtract the bottom equation from the top:
{ − ( z + y = 30 ) x + y = 43 ​ x − z = 13
We will now take this and the last equation as a system; this time, we will eliminate z by adding the two equations:
{ + ( x + z = 55 ) x − z = 13 ​ 2 x = 68
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

Answered by MsEHolt | 2024-06-24

To solve the problem, we let the numbers in the circles be x, y, and z. We derived the equations x + y = 43 , y + z = 30 , and x + z = 55 , leading to the solutions x=34, y=9, and z=21. Therefore, the numbers in the circles should be 34, 9, and 21 respectively.
;

Answered by MsEHolt | 2024-09-26