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. $\newline$ 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 $p(c+b)$ . $\newline$ Select all the expressions that also represent the price of the greeting cards and gift bags. $\newline$ Select all that apply $\newline$ A $p c+b$ $\newline$ B $(b+c) p$ $\newline$ (C) $p c+p b$ $\newline$ D] $p c b$ $\newline$ E I don't know

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Grade 8

Identify equivalent linear expressions: word problems

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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.

\newline

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)

\newline

Select all the expressions that also represent the price of the greeting cards and gift bags.

\newline

Select all that apply

\newline

p c+b

\newline

(b+c) p

\newline

(C)

p c+p b

\newline

p c b

\newline

E I don't know

Understand Expression: Understand the given expression $p(c+b)$ . $\newline$ The expression $p(c+b)$ represents the total price for $c$ greeting cards and $b$ gift bags, each at the same price $p$ . We can distribute the price $p$ across the sum of $c$ and $b$ to find equivalent expressions.
Distribute Price: Distribute the price $p$ across the sum of $c$ and $b$ . $p(c+b) = pc + pb$ This shows that the total price is the sum of the price of $c$ greeting cards and the price of $b$ gift bags.
Compare Options: Compare the distributed expression to the given options. $\newline$ Option A: $pc+b$ is not correct because it adds $b$ to the price of $c$ greeting cards, which does not represent the total price. $\newline$ Option B: $(b+c)p$ is correct because it is a rearrangement of $p(c+b)$ , which does not change the value. $\newline$ Option C: $pc+pb$ is correct because it is the distributed form of $p(c+b)$ . $\newline$ Option D: $pcb$ is not correct because it implies a multiplication of all three variables, which does not represent the total price. $\newline$ Option E: ＂I don't know＂ is not an expression that represents the price.