Question

solutions to real - world inequality problems quick check
lada has challenged herself to do at least 100 full push - ups this week. on sunday, she does 30 push - ups. her arms are sore, so she decides to do fewer push - ups on the remaining days of the week. she wants to do the same number of push - ups each day for the rest of the week. write and solve an inequality for the number of push - ups lada needs to do each day for the rest of the week to meet her goal of 100 push - ups. which answer choice best interprets the solution in the context of this problem? (2 point)

• lada needs to do at least 24 push - ups each day for the rest of the week to meet her goal.
• lada needs to do at least 10 push - ups each day for the rest of the week to meet her goal.
• lada needs to do push - ups for at least 10 more days to meet her goal.
• lada needs to do at least 12 push - ups each day for the rest of the week to meet her goal.

Explanation:

Step1: Define variables and total goal

Let $x$ = daily push-ups for remaining days.
Total goal: $100$ push-ups.
Sunday's push-ups: $30$.
Remaining days in week: $6$.

Step2: Set up inequality

Total push-ups = Sunday + 6 days of $x$, must be ≥ 100.
$30 + 6x \geq 100$

Step3: Isolate the variable term

Subtract 30 from both sides.
$6x \geq 100 - 30$
$6x \geq 70$

Step4: Solve for x

Divide both sides by 6.
$x \geq \frac{70}{6} \approx 11.67$
Since push-ups are whole numbers, $x \geq 12$.

Answer:

Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.