Question

lesson 15 session 3
4
olivia and isabella each earn d dollars for each dog she walks. one day, olivia walks 6 dogs and gets $8 in tips. that same day, isabella walks 9 dogs and gets $12 in tips.
a. olivia writes 6d + 8 + 9d + 12 to represent the amount they earn together. isabella writes 5(3d + 4). are their expressions equivalent? show your work.
dog walking
olivia
6 walks
$8 in tips
isabella
9 walks
$12 in tips

Explanation:

Step1: Simplify Olivia's expression

Olivia's expression is \(6d + 8 + 9d + 12\). Combine like terms: \( (6d + 9d) + (8 + 12) = 15d + 20\).

Step2: Simplify Isabella's expression

Isabella's expression is \(5(3d + 4)\). Use the distributive property: \(5\times3d + 5\times4 = 15d + 20\).

Step3: Compare the two simplified expressions

Both expressions simplify to \(15d + 20\), so they are equivalent.

Answer:

Yes, their expressions are equivalent.