Trying to find out how many miles it covered each day

Question

A hot air balloon covered 2,100 miles in 7 days. If it covered 50 miles more each day than before, how many miles did it cover each day?

Answer 1

Here's a simple solution.

2100 miles in 7 days

2100/7=300 miles per day on average

there are 7 days so the 4th day is the middle day when the balloon traveled 300 miles

each day the balloon traveled 50 more miles

300, 350, 400, 450

300, 250, 200, 150

150, 200, 250, 300, 350, 400, 450 for days 1,2,3,4,5,6, and 7

Answer 2

These equations sound a lot harder than they really are. Just start with the first day.

 

1. Since we do not know how many miles the balloon traveled on the first day, we will say it traveled x days.
2. Day 2 - It traveled the same amount (x) + 50 more miles. x + 50 miles.
3. Day 3 - It traveled the same amount as day 2 (x +50) + 50 more miles. x + 100
4. Day 4 - It traveled the same amount as day 3 (x +100) + 50 more miles. x + 150
5. Day 5 - It traveled the same amount as day 4 (x +150) + 50 more miles. x + 200
6. Day 6 - It traveled the same amount as day 5 (x +200) + 50 more miles. x + 250
7. Day 7 - It traveled the same amount as day 6 (x +250) + 50 more miles. x + 300

 

Then you add all the values and solve for x.

 

A trick I use when I have big math is group.

• You have 7 xs (one for each day)
• Then you have 50 + 100 + 150 + 200 + 250 + 300 extra miles on top.
• Work inward 50 +300 = 350, 100 + 250 = 350, 150 +200 = 350. So, you have 3 groups of 350. 3 * 350 = 1050.

 

So, 2100 miles = 7x + 1050.

• Subtract 1050 from each side and you are left with 7x = 1050.
• Divide both sides by 7 and x = 150.

 

So (numbers represent days)

1. traveled x miles. x = 150, so traveled 150 miles.
2. traveled x + 50 miles. x = 150, so traveled 200 miles.
3. traveled x + 100 miles. x = 150, so traveled 250 miles.
4. traveled x + 150 miles. x = 150, so traveled 300 miles.
5. traveled x + 200 miles. x = 150, so traveled 350 miles.
6. traveled x + 250 miles. x = 150, so traveled 400 miles.
7. traveled x + 300 miles. x = 150, so traveled 450 miles.

 

If you add and check, you will see that they all add up to 2100. It's long, but not as hard as it seems. Just take it one day at a time (just like life).

 

Have a good night, Ms. Maria.

Kyle J. Smith