WORKSHEET ON SOLVING LITERAL EQUATIONS

Solve the following literal equations

1)  Solve V = lwh for w

2)  Solve m = (y₂ - y₁)/(x₂ - x₁) for y₂

3)  Solve ax + by = c for y

4)  Solve A = (a + b + c + d)/4 for c

5)  Solve S = 2(lw + lh + wh) for w.

6)  Solve P = 2(l + w) for l

7)  Solve d = c/π for π

8)  Solve 5t - 2r = 25 for t

9)  Solve S = R - rR for R.

10)  Solve V = 1/3πh²(3r - h) for r

11)  Solve A = 1/2nal for n

12)  Solve (p₁v₁)/T₁ = (p₂v₂)/T₂ for T₁

13)  Solve F = (gm₁m₂)/d² for g

14)  Solve (12ds)/w = CD for w

15)  Solve A = 1/2bh for b

Solution

Problem 1 :

If X = (X + 1)/(Y + Z), find X in terms of Y and Z.

Solution

Problem 2 :

If x(y + 2) = y, find y in terms of x.

Solution

Problem 3 :

If a/b = (a + 1)/2c, find a in terms of b and c.

Solution

Problem 4 :

If t = (2/3)ax, find ax in terms of t.

Solution

Problem 5 :

If 3x + 6y = 7z, find x + 2y in terms of z.

Solution

Problem 6 :

If x + 5 = 2b, find 2x + 10 in terms of b.

Solution

Problem 7 :

If (a – 1)/2t = a, find 4t in terms of a.

Solution

Problem 8 :

If (p – h)/(p + h) = 2/3, find p/h.

Solution

Problem 9 :

If (1 + 2r)/(1 – t) = 1/2, find t in terms of r.

Solution

Problem 10 :

If x^y = z, then find x^2y in terms of z.

Solution

Problem 11 :

If (4^{x + 1})/(x³ – x²) = p(x⁵ – x⁴), what is p in terms of x ?

Solution

Problem 12 :

If 2^x(x³ – 1/x) = m(x² + 1) – 1/x², what is m in terms of x ?

Solution

Problem 13 :

If ((√x + 1)/(5x² – 3) – x³) = 1/nx, what is n in terms of x ?

Solution

Problem 14 :

If a(b² + 2) + c = 5(c + 1)³, what is a in terms of b and c ?

Solution

Problem 15 :

If k(x² + 4) + ky = (7x² + 3)/2, what is k in terms x and y ?

Solution

Problem 16 :

If ax + 3a + x + 3 = b, what is x in terms a and b ?

Solution

Problem 1 :

If one book costs c dollars, what is the cost, in dollars, of m books?

(A) m + c     (B) m/c      (C) c/m      (D) mc      (E) mc/100

Solution

Problem 2 :

Represent the cost, in dollars, of k pounds of apples at c cents per pound.

(A) kc     (B) 100kc     (C) kc/100

(D) 100k + c   (E) (k/100) + c

Solution

Problem 3 :

If p pencils cost c cents, what is the cost of one pencil?

(A) c/p     (B) p/c     (C) pc

(D) p - c   (E) p + c

Solution

Problem 4 :

Express the number of miles covered by a train in one hour if it covers r miles in h hours.

(A) rh    (B) h/r    (C) r/h (D) r + h      (E) r – h

Solution

Problem 5 :

Express the number of minutes in h hours and minutes.

(A) mh    (B) (h/60) + m    (C) 60(h + m)

(D) (h + m)/60    (E) 60h + m

Solution

Problem 6 :

Express the number of seats in the school auditorium if there are r rows with s seats each row and s rows with r seats each.

(A) 2rs    (B) 2r + 2s    (C) rs + 2

(D) 2r + s   (E) r + 2s

Solution

Problem 7 :

How many dimes are there in n nickels and q quarter ?

(A) 10nq    (B) (n + q)/10    (C) (1/2)n+(5/2)q

(D) 10n + 10q     (E) 2n + (q/10)

Solution

Problem 8 :

Roger rents a car at a cost of D dollars per day plus c cent per mile. How many dollars must he pay if he uses the car for 5 days  and drives 1000 miles ?

(A) 5D + 1000c    (B) 5D + (c/1000)   (C) 5D + 100c

(D) 5D + 10c     (E) 5D + c

Solution

Problem 9 :

The cost of a long-distance telephone call is c cents for the first three minutes and m cents for each additional minute. Represent the price of a call lasting d minutes if d is more than 3.

(A) c + md     (B) c + md – 3m     (C) c + md + 3m

(D) c + 3md      (E) cmd

Solution

Problem 10 :

The sales tax in Morgan country is m%. Represent the total cost of an article priced at $D.

A) D + mD    (B) D + 100mD     (C) D + mD/100

(D) D + m/100 (E) D + 100m

Solution