IM 7.6.17 Lesson: Modeling with Inequalities
[size=150]The stage manager of the school musical is trying to figure out how many sandwiches he can order with the $83 he collected from the cast and crew. Sandwiches cost $5.99 each, so he lets [math]x[/math] represent the number of sandwiches he will order and writes [math]5.99x\le83[/math]. He solves this to 2 decimal places, getting [math]x\le13.86[/math].[/size][br][br]Which of these are valid statements about this situation? (Select [b]all [/b]that apply.)
A mover is loading an elevator with many identical 48-pound boxes. The mover weighs 185 pounds. The elevator can carry at most 2000 pounds.
[size=150][size=100]Write an inequality that says that the mover will not overload the elevator on a particular ride. Check your inequality with your partner.[/size][/size]
Solve your inequality and explain what the solution means.
Graph the solution to your inequality on a number line.
If the mover asked, “How many boxes can I load on this elevator at a time?” what would you tell them?
[size=150]Your teacher will give you either a [i]problem card[/i] or a [i]data card[/i]. Do not show or read your card to your partner.[/size][br][table][tr][td]If your teacher gives you the [i]problem card[/i]:[/td][td]If your teacher gives you the [i]data card[/i]:[/td][/tr][tr][td][list=1][*]Silently read your card and think about what [br]information you need to be able to answer [br]the question.[br][/*][*]Ask your partner for the specific information [br]that you need.[br][/*][*]Explain how you are using the information to [br]solve the problem.[br]Continue to ask questions until you have enough [br]information to solve the problem.[br][/*][*]Share the [i]problem card [/i]and solve t[br]he problem independently.[br][/*][*]Read the [i]data card[/i] and discuss your reasoning.[br][/*][/list][/td][td][list=1][*]Silently read your card.[br][/*][*]Ask your partner [br][i]“What specific information do you need?”[/i] [br]and wait for them to [i]ask[/i] for information.[br]If your partner asks for information that [br]is not on the card, do not do the calculations for them. [br]Tell them you don’t have that information.[br][/*][*]Before sharing the information, ask [br]“[i]Why do you need that information?[/i]” [br]Listen to your partner’s reasoning and [br]ask clarifying questions.[br][/*][*]Read the [i]problem card[/i] and solve [br]the problem independently.[br][/*][*]Share the [i]data card[/i] and discuss your reasoning.[br][/*][/list][/td][/tr][/table]
In a day care group, nine babies are five months old and 12 babies are seven months old. How many full months from now will the average age of the 21 babies first surpass 20 months old?
IM 7.6.17 Pratice: Modeling with Inequalities
[size=150]28 students travel on a field trip. They bring a van that can seat 12 students. Elena and Kiran’s teacher asks other adults to drive cars that seat 3 children each to transport the rest of the students.[br][br]Elena wonders if she should use the inequality [math]12+3n>28[/math] or [math]12+3n\ge28[/math] to figure out how many cars are needed. Kiran doesn’t think it matters in this case. Do you agree with Kiran? Explain your reasoning.[/size]
In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.
5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and the fifth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 liters of water. Write an inequality whose solution is the possible size of each of the 4 barrels.
How are the last two problems similar?
How are they different?
Solve each equation.
[math]5(n-4)=\text{-}60[/math]
[math]\text{-}3t+\text{-}8=25[/math]
[math]7p-8=\text{-}22[/math]
[math]\frac{2}{5}(j+40)=\text{-}4[/math]
[math]4(w+1)=\text{-}6[/math]
Select [b]all[/b] the inequalities that have the same graph as [math]x<4[/math].
A 200 pound person weighs 33 pounds on the Moon.
How much did the person’s weight decrease?
By what percentage did the person’s weight decrease?