QuestionFind an equivalent expression for the total cost of gift cards: $14 \ell + 42 a$ .

Studdy Solution

STEP 1

Assumptions1. Each lawyer gets a gift card worth $\$ \ell$ . . Each assistant gets a gift card worth $\$ a$ .
3. There are14 lawyers.
4. Each lawyer has3 assistants.
5. The expression for the total cost of the gift cards is $14 \ell+42 a$ .

STEP 2

We are asked to find an equivalent expression to $14 \ell+42 a$ . An equivalent expression is one that has the same value for all values of the variables.

STEP 3

We can factor out the common factor from the given expression. The common factor here is14.
$14 \ell+42 a =14(\ell+3a)$

STEP 4

Now, we can interpret the factored expression. The term $\ell+3a$ represents the total cost of gift cards for one lawyer and his/her3 assistants.Therefore, the equivalent expression to $14 \ell+42 a$ is $14(\ell+3a)$ , which represents the total cost of gift cards for14 lawyers and their assistants.

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