Answer :
To find the real-world problem that can be modeled by the equation [tex]\(d - 175 = 225\)[/tex], let's solve for [tex]\(d\)[/tex].
1. Start with the equation:
[tex]\[
d - 175 = 225
\][/tex]
2. To isolate [tex]\(d\)[/tex], add 175 to both sides of the equation:
[tex]\[
d = 225 + 175
\][/tex]
3. Calculate the sum:
[tex]\[
d = 400
\][/tex]
This tells us that the total distance of the Shaws' trip is 400 miles. Now, let's match this result with one of the statements given in the question:
- Option 1: "The Shaws drove 225 miles. They are 175 miles away from their destination."
- This suggests a trip total of [tex]\(225 + 175 = 400\)[/tex] miles, which matches our calculation.
- Option 2: "The Shaws drove 175 miles. There are 225 miles remaining in their drive."
- This suggests a trip total of [tex]\(175 + 225 = 400\)[/tex] miles, which also matches our calculation.
- Option 3: "The Shaws' trip is 225 miles and they've driven 175 miles."
- This suggests a trip total of 225 miles, which does not match our calculation.
- Option 4: "The Shaws' trip is 175 miles. They drove 225 miles."
- This suggests an inconsistency since they cannot drive more miles than the trip's total.
Based on our calculation, options 1 and 2 correctly describe a scenario where the total trip is 400 miles. However, the most straightforward match to the equation provided, where [tex]\(d - 175 = 225\)[/tex], aligns with option 1: "The Shaws drove 225 miles. They are 175 miles away from their destination."
1. Start with the equation:
[tex]\[
d - 175 = 225
\][/tex]
2. To isolate [tex]\(d\)[/tex], add 175 to both sides of the equation:
[tex]\[
d = 225 + 175
\][/tex]
3. Calculate the sum:
[tex]\[
d = 400
\][/tex]
This tells us that the total distance of the Shaws' trip is 400 miles. Now, let's match this result with one of the statements given in the question:
- Option 1: "The Shaws drove 225 miles. They are 175 miles away from their destination."
- This suggests a trip total of [tex]\(225 + 175 = 400\)[/tex] miles, which matches our calculation.
- Option 2: "The Shaws drove 175 miles. There are 225 miles remaining in their drive."
- This suggests a trip total of [tex]\(175 + 225 = 400\)[/tex] miles, which also matches our calculation.
- Option 3: "The Shaws' trip is 225 miles and they've driven 175 miles."
- This suggests a trip total of 225 miles, which does not match our calculation.
- Option 4: "The Shaws' trip is 175 miles. They drove 225 miles."
- This suggests an inconsistency since they cannot drive more miles than the trip's total.
Based on our calculation, options 1 and 2 correctly describe a scenario where the total trip is 400 miles. However, the most straightforward match to the equation provided, where [tex]\(d - 175 = 225\)[/tex], aligns with option 1: "The Shaws drove 225 miles. They are 175 miles away from their destination."
