Question

Jacob decided to ride his bicycle across the country during his 2-month summer vacation. the route he took from washington, dc to portland, oregon, covered a total of 2800 miles. to keep his mind occupied during some of the long flat stretches of countryside, he often did algebra problems in his head. one day, for example, he determined that his distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point. how far was jacob from the finishing point of his journey when he made that calculation? start your work by defining the unknown quantities in terms of one variable. show all work and write a complete answer, including units

Answer 1

Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)

Step 2: Use the sentence given to set up an equation

Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"

Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.

Using the sentence we can write the below equation...

$x = 100 + 3(2800 - x)$

Distributing 3 in the right side of the equation, we get...

$x = 100 + 8400 - 3x$

Adding 3x on both sides of the equation, we get...

$x+3x = 8500$

Combine like terms in the left side of the equation, we get...

$4x=8500$

Dividing 4 on both sides of the equation, we get...

$\frac{4x}{4} =\frac{8500}{4}$

Simplifying the fraction on either side of the equation, we get...

$x=2125miles$

Conclusion:

Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be 675 miles.