Question

Suppose your school is selling magazine subscriptions. Each subscription costs 20$. The company pays the school half the total sales in dollars the school must also pay a one time fee of $18 right and solve an equation to determine the fewest numbers of subscriptions that can be sold to earn a profit of $200

Answer 1

Answer: 22

Step-by-step explanation:

One subscription costs $20, we can say $x$ number of subscriptions will cost 20$x$.

(Eg. 1 subscription is $20, 2 subscriptions will be $40, 3 subscriptions will be $60 and so on.)

The school receives half of the total sales. That means if the total sales is 20$x$, the school will receive:  $\frac{20x}{2}$

The school will have to pay $18 once, that means: $\frac{20x}{2}$ -18 is the net amount the school will receive.

This amount must be greater than or equals to $200, we can convert this statement in an equation: $\frac{20x}{2}$ -18 ≥ 200

We solve this inequality. Remember, when solving the inequality you treat the sign similar to an equals to sign. That means all operations (subtraction, addition, change of sign are according to the same rules.)

$\frac{20x}{2}$ -18 ≥ 200

(solve the fraction first)

10$x$-18 ≥ 200

10$x$ ≥ 200+18 (bring 18 to the other side of the inequality, hence sign change)

10$x$ ≥ 218

$x$ ≥ 218/10 (divide the entire inequality by 10)

$x$ ≥ 21.8

Number of subscriptions will always be a whole number. Hence the lowest possible whole number that satisfies the inequality is 22.