1. **Problem statement:** We have three circles arranged in a triangle, with three squares between each pair of circles. Each square contains a number representing the sum of the two adjacent circles. The squares have values 150, 130, and 120. We need to find the numbers in the three circles. 2. **Define variables:** Let the numbers in the three circles be $x$, $y$, and $z$. 3. **Write equations from the problem:** - The square between circles with numbers $x$ and $y$ is 150, so: $$x + y = 150$$ - The square between circles with numbers $y$ and $z$ is 130, so: $$y + z = 130$$ - The square between circles with numbers $z$ and $x$ is 120, so: $$z + x = 120$$ 4. **Solve the system of equations:** Add all three equations: $$ (x + y) + (y + z) + (z + x) = 150 + 130 + 120 $$ $$ 2(x + y + z) = 400 $$ Divide both sides by 2: $$ \cancel{2}(x + y + z) = \cancel{2}200 $$ $$ x + y + z = 200 $$ 5. **Find each variable:** From $x + y = 150$, substitute $y = 150 - x$ into $x + y + z = 200$: $$ x + (150 - x) + z = 200 $$ $$ 150 + z = 200 $$ $$ z = 200 - 150 = 50 $$ From $y + z = 130$: $$ y + 50 = 130 $$ $$ y = 130 - 50 = 80 $$ From $z + x = 120$: $$ 50 + x = 120 $$ $$ x = 120 - 50 = 70 $$ 6. **Final answer:** The numbers in the circles are: $$ x = 70, \quad y = 80, \quad z = 50 $$