Solving Equations & Transforming Formulas

Formula Transformation
Formula transformation refers to the process of rearranging a formula in order to isolate a designated variable. The process of rearranging the formula follows the same principles and steps as those for solving linear equations. Once again, you are asked to arrive at an equation that contains the designated variable (with an understood positive one numerical coefficient) on one side of the equal sign and everything else on the other. Study the examples below then work e practice problems on the reverse of this page.

Solve for S :
M = S - C
M + C = S - C + C	Add C to both sides to isolate S.
M + C = S	The coefficient of S is positive one, so formula is solved.
S = M + C	S is rewritten on left for convenience.
Solve for R :
I=PRT	Since we are solving for R , PT can be viewed as its coefficient .
	Divide both sides by the coefficient of the variable R.
	Rewrite with R on the left.
Solve for n :
A = P(1 + ni)	Use the distributive principle to remove parentheses.
A = P + Pni	Subtract P to isolate the term containing n.
A - P = P + Pni - P
	Divide both sides by Pi, the coefficient of n.
	Rewrite.
Solve for a
	Isolate a2 by subtracting b2 from both sides.
	Take the square root of both sides.
	Rewrite.

Formula transformation exercises. Solve for the indicated variable.

1. v₂ = v₁ + at, for v₁

2. PV = RT, for T

3. I = (5300CE)/ d², for C

4. L = yd / mR, for R

5. L = L₀(1 + at), for a

6. A = 180 - (B + C), for B

7. L = 3.14 (r₁ + r₂) + 2d, for r₁

8. p - p_a = dg(y₂ - y₁) , for y₂

9. A = (n₁p₁ + n₂p₂) / (n₁ +n₂), for p₁

10. f = (f_su) / (u + v_s), for v_s

For the following transformation exercises, first re- arrange the formula , then solve for the unknown (even though this can be solved another way).

11. Solve for T. Find T when Q = 250, W = 125, and L = 20.

12. Solve C = 2πr for r. Find r when C = 154 and π = 22/7

13. Solve for F. Find F if C = 100°.

14. Solve S = πrs for s. Find s when S = 4352, π = 3.14, and r = 462.

15. Solve i = prt for r. Find r when i = $80, p = $500, and t = 2 years.

16. Solve p = a + b + c for c. Find c when p = 100, a = 21, and b =17.

17. Solve Q = 0.000477EIT for T. Find T when Q = 954, E = 1,000, and I = 20.

18. Solve L = π rA/180 for A. Find A when L = 314, r = 60, and π = 3.14.

19. Solve T = 2B + pH for H. Find H when T = 860, B = 45, and p = 11.

20. Solve C = πd for d. Find d when C = 120 feet and π = 3.14, to the nearest hundredth.

21. Solve T = 1/2ps + B for B. Find B when T = 580, p = 58, and s = 12.

ANSWERS