Question

puzzle #3
1: solve for c:
$abcd = e$
2: solve for c:
$a - b + cd = e$
3: solve for c:
$\frac{a + bc}{d} = e$
4: solve for c:
$\frac{ab}{c} = de$
answer choices
a: $\frac{de - a}{b}$ b: $\frac{ade}{b}$ c: $\frac{ab}{de}$
d: $\frac{de}{ab}$ e: $de - ab$ f: $\frac{a - b}{de}$
g: $\frac{e}{abd}$ h: $dae + b$ i: $\frac{e - a + b}{d}$
type the 4-letter code into the answer box. all caps, no spaces.
your answer

Explanation:

Step1: Isolate $c$ (Problem 1)

Start with $abcd = e$. Divide both sides by $abd$:
$\frac{abcd}{abd} = \frac{e}{abd}$
Simplify to get $c = \frac{e}{abd}$, which matches option G.

Step2: Isolate $c$ (Problem 2)

Start with $a - b + cd = e$. Subtract $a-b$ from both sides:
$cd = e - a + b$
Divide by $d$:
$c = \frac{e - a + b}{d}$, which matches option I.

Step3: Isolate $c$ (Problem 3)

Start with $\frac{a + bc}{d} = e$. Multiply both sides by $d$:
$a + bc = de$
Subtract $a$:
$bc = de - a$
Divide by $b$:
$c = \frac{de - a}{b}$, which matches option A.

Step4: Isolate $c$ (Problem 4)

Start with $\frac{ab}{c} = de$. Cross-multiply:
$ab = c \cdot de$
Divide by $de$:
$c = \frac{ab}{de}$, which matches option C.

Answer:

G I A C
4-letter code: GIAC