Question

Olivia and Isabel each earn D dollars for each dog she walks. One day, Olivia walks six dogs and gets eight dollars in tips. The same day, Isabell walks nine dogs and gets $12 in tips. Olivia Wright, 6d+8+9d+12 to represent the amount they earn together. Isabell right 5(d+4) are there expressions equivalent? Show your work.

Answer 1

No

Explanation:

Step 1) 6d+8+9d+12

Step 2) 15d+20=5(d+4)

Step 3) 5(3d+4)≠5(d+4)

Answer 2

No

Explanation:

You want to know if Olivia's expression 6d +8 +9d +12 is equivalent to Isabell's expression 5(d +5).

Olivia

We can rewrite Olivia's expression as ...

6d +8 +9d +12 = (6d +9d) +(8 +12) = (6 +9)d +20 = 15d +20

= 5·3d +5·4

= 5(3d +4)

Equivalence

The expression 5(3d +4) is not equivalent to Isabell's expression 5(d +4).

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Additional comment

Alternatively, we could expand Isabell's expression to 5d +20, which may be easier to see is not equivalent to 15d +20.

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