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 $pc+b$ $\newline$ B $(b+c)p$ $\newline$ C $pc+pb$ $\newline$ D $pcb$ $\newline$ E I don't know

View step-by-step help

Home

Math Problems

Grade 8

Identify equivalent linear expressions: word problems

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.

\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

pc+b

\newline

(b+c)p

\newline

pc+pb

\newline

pcb

\newline

E I don't know

Understand given expression: Understand the given expression $p(c+b)$ . This expression indicates that the price of the greeting cards and gift bags is the product of the price per item ( $p$ ) and the sum of the number of greeting cards ( $c$ ) and gift bags ( $b$ ) purchased.
Evaluate option A: Evaluate option A $(pc+b)$ . This expression suggests adding the price of one greeting card $(pc)$ to the number of gift bags $(b)$ , which does not account for the price per gift bag. This is not equivalent to the given expression $p(c+b)$ .
Evaluate option B: Evaluate option B $(b+c)p$ . This expression is the same as the given expression $p(c+b)$ but written with the factors in reverse order. Multiplication is commutative, so this expression is equivalent to the given expression.
Evaluate option C: Evaluate option C $p_c+p_b$ . This expression represents the price of $c$ greeting cards $p_c$ plus the price of $b$ gift bags $p_b$ , which is equivalent to the given expression $p(c+b)$ since it distributes the price $p$ over the sum of $c$ and $b$ .
Evaluate option D: Evaluate option D $(pcb)$ . This expression suggests multiplying the price $(p)$ by both the number of greeting cards $(c)$ and the number of gift bags $(b)$ , which implies a multiplication of three quantities rather than adding the number of items. This is not equivalent to the given expression $p(c+b)$ .
Evaluate option E: Evaluate option E (I don't know). This is not an expression but an indication of uncertainty. It does not represent the price of the greeting cards and gift bags.