Question

1. you and your friend are planning to walk across an old bridge. the bridge can hold at most 1000 pounds. the total weight of the people currently on the bridge is 625 pounds. you weigh 156 pounds.

a. write and solve an inequality that represents how much your friend can weigh within the limits of the bridge.
b. your friend weighs 182 pounds. can you and your friend both walk on the bridge? explain.

1. the school baseball record for no - hitter innings is 112 in a season. this year the team currently has 87 no - hitter innings. what are the possible numbers of additional no - hitter innings the team can achieve to match or break the school record in a season?
2. which of the following inequalities are equivalent to the inequality 5 < h where h is a constant? select all that apply. justify your answer.

a. 5 + y+ b < 0
b. y < h - 5
d. 5 - 5 < y
c. b - 5 > 5

Explanation:

Step1: Set up the inequality for question 17a

Let $x$ be the weight of the friend. The sum of the current weight on the bridge, your weight, and your friend's weight must be less than or equal to the bridge's capacity. So the inequality is $625 + 156+x\leq1000$.

Step2: Simplify the left - hand side of the inequality

$625+156 = 781$, so the inequality becomes $781 + x\leq1000$.

Step3: Solve for $x$

Subtract 781 from both sides of the inequality: $x\leq1000 - 781$, so $x\leq219$.

Step4: Answer question 17b

Find the total weight of you and your friend: $156+182 = 338$ pounds. The total weight of people currently on the bridge and you and your friend is $625+338=963$ pounds. Since $963\leq1000$, you and your friend can both walk on the bridge.

Step5: Answer question 18

Let $x$ be the additional number of no - hitter innings. The team's current number of no - hitter innings plus the additional innings must be greater than or equal to the school record. So the inequality is $87+x\geq112$. Subtract 87 from both sides: $x\geq112 - 87$, so $x\geq25$.

Step6: Answer question 19

Start with the inequality $5 + y+b\leq0$. Solve for $y$: $y\leq - b - 5$.

• For option a: $5 + y + b\leq0$ is the original inequality we can work from.
• For option b: $y\lt b - 5$ is not equivalent.
• For option c: $b-5\geq y$ can be rewritten as $y\leq b - 5$ which is not equivalent.
• For option d: $b - 5\lt y$ is not equivalent.

Answer:

17a. The inequality is $625 + 156+x\leq1000$ and the solution is $x\leq219$.
17b. Yes, because the total weight of people on the bridge when you and your friend walk on it is $625+156 + 182=963$ pounds and $963\leq1000$.

1. $x\geq25$
2. a. $5 + y + b\leq0$