2.8 - Literal Equations

Basic Literal Equations

100

Solve for b:

b - 18a = c

b = c + 18a

200

Solve for q:

aqz = b

q = b/az

300

Solve for x:

xy/d = 2

x = 2d/y

400

Solve for w:

4x/7w = 8/9

x = 14/9w

500

Solve for y

A = 1/2(h)(x + y)

(2A - hx)/h = y

Real-World Formulas

100

Distance formula

Solve for t: 

d = rt

t = d/r

200

Perimeter of a Rectangle

Solve for w

P = 2l + 2w

w = (P - 2l)/2

300

Converting Fahrenheit into Celsius

Solve for F

C = 5/9(F - 32)

F = 9/5C + 32

400

Volume of a cone

Solve for h:

V = 1/3(π)(r²)(h)

h = 3V/(π)(r²)

500

Kinetic Motion Equation

Solve for a: 

d-v_it = 1/2at²

*v_i stands for inital velocity, _i is not a variable.

a = 2(d-v_it)/t²

Word Problems

100

The perimeter of a square is P=4s where P is the perimeter and s is the side length. Write an equation to find out the side length (s) if you know the perimeter.

s=P/4

200

A taxi company uses this formula to calculate the amount of money (d) they make: d = 2.5m + 5. m stands for miles. Solve the formula for the number of miles driven (m).

m=d-5/2.5

300

The formula to find a student's average grade (a) across three tests is: A = (x + y + z)/3 

Solve the equation to find the student's score on the third test (z). 

z = 3A - x - y

400

The surface area (S) of a cylinder is given by S=2πrh + 2πr². If you know the area of the circular bases, you can look at the lateral area: L=2πrh. Solve the lateral area formula for height (h). If the diameter of the cylinder is 8, and the lateral area is 37.68, what is the height? Use 3.14 for π.

Hint: The diameter is double the radius or 2R = D

h = L/2πr

h = 1.5 units

500

A chemist is mixing two flammable chemicals (chemical a and chemical b) together. The formula to calculate the amount of heat produced is H = (3k - 2r)/t, where H is the amount of heat produced in Joules, k is the concentration of chemical a, r is the chemical b, and t is the amount of time the experiment has been active in minutes. Solve the equation for r and figure out what the concentration of chemical b is if the heat is 30, chemical a's concentration is 10, and the time is has been running for is 2 minutes.

r = (Ht - 3k)/-2

Chemical a's concentration is -15 

Challenge Problems

100

Solve for x:

2(x² + y²) = 4b

x = ±√2b - y²

200

Solve for g:

2/3hg = 5/(x^2)

g = 15/(2hx²)

h ≠ 0

x ≠ 0

300

Surface Area of a cylinder:

Solve for h:

A =  2πr² + 2πrh

h = (A -  2πr²)/ 2πr

400

Solve for y:

A(x - y) = B(x + y) + C

y = (Ax - Bx - C)/(A + B)

500

Quadratic Formula

Solve for c:

x  = (-b ± √b² - 4ac)/2a

c = -ax² - bx