Question

A salesman used three types of order forms: A, B, C. He used 40 of Form A. Of Form B he used four times as many as Form A plus 1/2 as many as Form C. He used as many of Form C as Form A plus 1/2 as many as Form B. Altogether, how many forms did he use? Clear 0A. 440 B. 200 C. 250 D. 320 E. 500

Answer 1

Answer:

The correct option is A. 440

Step-by-step explanation:

Let a, b and c represents the number of orders from forms A, B and C,

According to the question,

$a = 40$,

$b = 4a + \frac{1}{2}c$

$c = a + \frac{1}{2}c$

From these equations we get,

$b = 160 + \frac{1}{2}c----(1)$

$c = 40 + \frac{1}{2}b---(2)$

Substitute the value of b from (1) to (2),

$c = 40 + \frac{1}{2}(160 + \frac{1}{2}c)$

$c = 40 + 80 + \frac{1}{4}c$

$c-\frac{1}{4}c = 120$

$\frac{4c-c}{4}=120$

$\frac{3c}{4}=120$

$c=\frac{480}{3}=160$

From (1),

$b = 160 + \frac{1}{2}(160)=160 + 80 = 240$

$\because a + b + c = 40 + 240 + 160 = 440$

Hence, he used 440 forms total,

i.e. OPTION A is correct.