Let's break down the problem step-by-step to understand how to express Dale's money in terms of the amount of money Leo has.
1. Understanding the Relationship:
- Leo has [tex]\( d \)[/tex] dollars.
- Dale has three dollars more than twice the amount of money that Leo has.
2. Expressing in Mathematical Terms:
- First, find "twice the amount of money that Leo has": This is [tex]\( 2d \)[/tex].
- Next, add three dollars to this amount: This gives us [tex]\( 2d + 3 \)[/tex].
3. Forming the Expression:
- We have determined that Dale's amount of money in terms of Leo's amount is [tex]\( 2d + 3 \)[/tex].
4. Evaluating the Given Options:
- Option 1: [tex]\( 2(3) + d \)[/tex]:
- This expands to [tex]\( 6 + d \)[/tex], which is incorrect because it's not based on the correct relationship stated in the problem.
- Option 2: [tex]\( \frac{d}{2} + 3 \)[/tex]:
- This suggests Dale has half of Leo's money plus three, which does not match the problem description.
- Option 3: [tex]\( 2d + 3 \)[/tex]:
- This correctly represents "twice the amount of money that Leo has plus three," matching our earlier derivation.
- Option 4: [tex]\( d + 2 + 3 \)[/tex]:
- This simplifies to [tex]\( d + 5 \)[/tex], which again does not match the relationship described.
The correct statement is:
If Leo has [tex]\( d \)[/tex] dollars, then Dale has [tex]\( 2d + 3 \)[/tex] dollars.
