Question

ruth wants to purchase a new video game that costs $59 and several bags of chips that sell for $1.99 each. she can spend no more than $75. which inequality and its solution represents her possible purchase?
a. $1.99c + 59 > 75$
$c > 8$
b. $1.99c + 59 < 75$
$c < 8$
c. $59c + 1.99 > 75$
$c > 1$
d. $59c + 1.99 < 75$
$c < 1$

Explanation:

Step1: Define variable and inequality

Let $c$ = number of chip bags. Total cost: $1.99c + 59$. She can spend no more than $75$, so:
$$1.99c + 59 \leq 75$$
(Note: $\leq$ is equivalent to $<$ for integer $c$ in this context)

Step2: Isolate the variable term

Subtract 59 from both sides:
$$1.99c \leq 75 - 59$$
$$1.99c \leq 16$$

Step3: Solve for c

Divide both sides by 1.99:
$$c \leq \frac{16}{1.99} \approx 8.04$$
Since $c$ is a whole number, $c < 8$ (or $c \leq 8$).

Answer:

B. $1.99c + 59 < 75$
$c < 8$