Asksia AI LOGO


Posted 3 months ago

Vince went on a 3 day hiking trip. Each day, he walked 34\frac{3}{4} the distance that he walked the day before. He walked 83.25 kilometers total in the trip.

How far did Vince walk on the 1st 1^{\text {st }} day of the trip?
Round your final answer to the nearest kilometer.
Sign in to unlock the answer
Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
Let's denote the distance Vince walked on the first day as dd
step 2
On the second day, Vince walked 34d\frac{3}{4}d
step 3
On the third day, Vince walked 34\frac{3}{4} of the distance of the second day, which is 34×34d=(34)2d\frac{3}{4} \times \frac{3}{4}d = \left(\frac{3}{4}\right)^2 d
step 4
The total distance walked over the three days is the sum of the distances walked each day: d+34d+(34)2dd + \frac{3}{4}d + \left(\frac{3}{4}\right)^2 d
step 5
This sum equals the total distance walked, which is 83.25 km: d+34d+(34)2d=83.25d + \frac{3}{4}d + \left(\frac{3}{4}\right)^2 d = 83.25
step 6
Solving for dd, we combine like terms: d(1+34+(34)2)=83.25d \left(1 + \frac{3}{4} + \left(\frac{3}{4}\right)^2\right) = 83.25
step 7
Calculating the coefficient of dd: 1+34+(34)2=44+34+916=1616+1216+916=37161 + \frac{3}{4} + \left(\frac{3}{4}\right)^2 = \frac{4}{4} + \frac{3}{4} + \frac{9}{16} = \frac{16}{16} + \frac{12}{16} + \frac{9}{16} = \frac{37}{16}
step 8
The equation becomes 3716d=83.25\frac{37}{16}d = 83.25
step 9
Dividing both sides by 3716\frac{37}{16} to solve for dd: d=83.253716=83.25×1637d = \frac{83.25}{\frac{37}{16}} = \frac{83.25 \times 16}{37}
step 10
Calculating the value of dd: d=133237=36d = \frac{1332}{37} = 36
step 11
Rounding dd to the nearest whole number, we get d=36d = 36 km
Vince walked 36 km on the first day of his trip.
Key Concept
Geometric Series and Solving Equations
The distance walked each day forms a geometric series with a common ratio of 34\frac{3}{4}. To find the distance walked on the first day, we set up an equation based on the total distance and solve for the first term of the series.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question