Question

in a study of gaming habits, 420 males between the ages of 18 and 50 were surveyed and 380 females between the ages of 18 and 50 were surveyed. if 75 more females are surveyed, how many more males must be surveyed so that $\frac{2}{3}$ of the total number of gamers are male?

Explanation:

Step1: Define variable for new males

Let $x$ = number of additional males surveyed.

Step2: Calculate new female count

New female total: $380 + 75 = 455$

Step3: Set up proportion equation

Males are $\frac{2}{3}$ of total:
$$\frac{420 + x}{(420 + x) + 455} = \frac{2}{3}$$

Step4: Cross-multiply to solve for $x$

$$3(420 + x) = 2(875 + x)$$
$$1260 + 3x = 1750 + 2x$$

Step5: Isolate $x$

$$3x - 2x = 1750 - 1260$$
$$x = 490$$

Answer:

490