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Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Greeting cards ( 
c ) and gift bags (b) are the same price (p). Cassie purchased greeting cards and gift bags, the price of which can be expressed by 
p(c+b).
Select all the expressions that also represent the price of the greeting cards and gift bags.
Select all that apply
A 
pc+b
B 
(b+c)p
(C) 
pc+pb
D] 
pcb
E I don't know

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.\newlineGreeting cards ( c c ) and gift bags (b) are the same price (p). Cassie purchased greeting cards and gift bags, the price of which can be expressed by p(c+b) p(c+b) .\newlineSelect all the expressions that also represent the price of the greeting cards and gift bags.\newlineSelect all that apply\newlineA pc+b p c+b \newlineB (b+c)p (b+c) p \newline(C) pc+pb p c+p b \newlineD] pcb p c b \newlineE I don't know

Full solution

Q. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.\newlineGreeting cards ( c c ) and gift bags (b) are the same price (p). Cassie purchased greeting cards and gift bags, the price of which can be expressed by p(c+b) p(c+b) .\newlineSelect all the expressions that also represent the price of the greeting cards and gift bags.\newlineSelect all that apply\newlineA pc+b p c+b \newlineB (b+c)p (b+c) p \newline(C) pc+pb p c+p b \newlineD] pcb p c b \newlineE I don't know
  1. Understand Expression: Understand the given expression p(c+b)p(c+b).\newlineThe expression p(c+b)p(c+b) represents the total price for cc greeting cards and bb gift bags, each at the same price pp. We can distribute the price pp across the sum of cc and bb to find equivalent expressions.
  2. Distribute Price: Distribute the price pp across the sum of cc and bb.p(c+b)=pc+pbp(c+b) = pc + pbThis shows that the total price is the sum of the price of cc greeting cards and the price of bb gift bags.
  3. Compare Options: Compare the distributed expression to the given options.\newlineOption A: pc+bpc+b is not correct because it adds bb to the price of cc greeting cards, which does not represent the total price.\newlineOption B: (b+c)p(b+c)p is correct because it is a rearrangement of p(c+b)p(c+b), which does not change the value.\newlineOption C: pc+pbpc+pb is correct because it is the distributed form of p(c+b)p(c+b).\newlineOption D: pcbpcb is not correct because it implies a multiplication of all three variables, which does not represent the total price.\newlineOption E: "I don't know" is not an expression that represents the price.

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