On a three day hike, Robert hiked twice as many miles on the first day as on the second day. On the third day he hiked 5 miles. Carlos hiked 5 miles on the first day and three times as many miles on the second day as on the third day.
(a) Write and simplify an expression for the total number of miles Matthew hiked.
(b) Matthew hiked 6 miles on the second day. How many miles did Matthew hike in all?
(c) If Carlos hiked 4 miles on the third day, which boy hiked a greater total distance? Explain.
For part (a), I wrote x (2) + 5 = x
For part (b), I wrote 6 + 5 = 11 miles
For part (c), I wrote Carlos, because 15 + 4 = 19. If this is not correct, please help me?
I see Robert and Carlos but who is Matt?
For part (a), it seems you made a small mistake in writing the expression. Let's correct it:
- Robert hiked twice as many miles on the first day as on the second day. So, if we let "m" represent the number of miles Robert hiked on the second day, then the number of miles he hiked on the first day is 2m.
- On the third day, Robert hiked 5 miles.
To find the total number of miles Robert hiked, we add the distances from each day together:
Total miles = Hiked on the first day + Hiked on the second day + Hiked on the third day
Total miles = 2m + m + 5
Simplifying, we get: Total miles = 3m + 5
For part (b), you correctly calculated the number of miles Robert hiked on the second day as 6. To find the total number of miles he hiked, we substitute this value into the expression we derived in part (a):
Total miles = 3m + 5
Substituting m = 6, we get: Total miles = 3(6) + 5
Simplifying, we find: Total miles = 23 miles
For part (c), you predicted that Carlos hiked a greater total distance by comparing the sums of their distances. However, to determine the greater total distance, we need to compare the total miles hiked by Carlos and Robert, not Robert and Carlos. Let's calculate their total distances:
- For Robert:
We can use the expression we derived in part (a):
Total miles = 3m + 5
Substituting m = 6, we have: Total miles = 3(6) + 5 = 23 miles
- For Carlos:
On the first day, Carlos hiked 5 miles. On the second day, he hiked three times as many miles as on the third day, which is 4. So, Carlos hiked a total of: 5 + 3(4) = 5 + 12 = 17 miles
Comparing the total distances, we can see that Robert hiked a greater total distance than Carlos.