1. **State the problem:** Oscar thinks of a number $r$. He squares it to get $r^2$, multiplies by 4 to get $4r^2$, divides by 3 to get $\frac{4r^2}{3}$, then adds 7 to get 55. We need to find $r$. 2. **Write the equation:** $$\frac{4r^2}{3} + 7 = 55$$ 3. **Isolate the term with $r^2$:** Subtract 7 from both sides: $$\frac{4r^2}{3} = 55 - 7$$ $$\frac{4r^2}{3} = 48$$ 4. **Clear the denominator:** Multiply both sides by 3: $$4r^2 = 48 \times 3$$ $$4r^2 = 144$$ 5. **Solve for $r^2$:** Divide both sides by 4: $$r^2 = \frac{144}{4}$$ $$r^2 = 36$$ 6. **Find $r$:** Take the square root of both sides: $$r = \pm \sqrt{36}$$ $$r = \pm 6$$ **Final answer:** $r = 6$ or $r = -6$