Question

1. sylvie needs $110.75 for a concert ticket. she already has $16 and she can earn the rest by working 10.5 hours at her job. write an equation that can be solved to find h, sylvies hourly earnings.
2. on a road trip, a family drives 350 miles per day. how many days, d, must they travel to reach a distance of at least 1,400 miles?

part a
write an inequality to represent this situation.
part b
solve the inequality. what does the solution represent in this situation?

1. natalie budgets $146 for yoga training. she buys a yoga mat for $10.65 and pays $9 per yoga class. write an inequality to represent the number of classes, c, that natalie can take and stay within her budget.
2. xander needs to collect at least 120 cans for a food drive to earn community service credit. he has already collected 64 items.

part a
write and solve an inequality to represent the number of cans, c, that xander must still collect.
part b
graph the solution on a number line and describe the solutions

Explanation:

Step1: Write the inequality for the family's road - trip

The family drives \(350\) miles per day. Let \(d\) be the number of days. The total distance they cover in \(d\) days is \(350d\) miles. They need to reach at least \(1400\) miles. So the inequality is \(350d\geq1400\).

Step2: Solve the inequality

Divide both sides of the inequality \(350d\geq1400\) by \(350\).

$$
LATEXBLOCK0
$$

The solution \(d\geq4\) means that the family must travel for \(4\) or more days to cover at least \(1400\) miles.

Step3: Write and solve the inequality for Xander's cans

Xander needs to collect at least \(120\) cans. He has already collected \(64\) cans. Let \(c\) be the number of cans he still needs to collect. Then the inequality is \(c + 64\geq120\).
Subtract \(64\) from both sides:

$$
LATEXBLOCK1
$$

Answer:

1. \(110.75=16 + 10.5h\)

2.

• Part A: \(350d\geq1400\)
• Part B: \(d\geq4\), which means the family must travel for 4 or more days.

1. \(146\geq9c + 10.65\)

4.

• Part A: \(c + 64\geq120\), \(c\geq56\)
• Part B: On a number line, we draw a closed circle at \(56\) (because \(c\) can be equal to \(56\)) and shade to the right. The solutions are all real numbers \(c\) such that \(c\) is greater than or equal to \(56\).