SOLUTION: Jack decided to ride his bicycle across the country during his 3-month summer vacation. The
route he took from Washington, DC to Portland, Oregon, covered a total of 3500 miles. T
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Question 1006140: Jack decided to ride his bicycle across the country during his 3-month summer vacation. The
route he took from Washington, DC to Portland, Oregon, covered a total of 3500 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 80 miles more than twice the distance remaining until the finishing point.
How far was Jack from the finishing point of his journey when he made that calculation? Start
your work by defining the unknown quantities in terms of a variable.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
One day, for example, he determined that his distance from his starting
point was exactly 80 miles more than twice the distance remaining until the finishing point.
How far was Jack from the finishing point of his journey when he made that calculation?
x = distance remaining to finish point.
2x + 80 = distance from start point.
total distance = x + 2x + 80.
total distance = 3500
3500 = x + 2x + 80
combine like terms to get 3500 = 3x + 80
subtract 80 from both sides of the equation to get 3420 = 3x
divide both sides of the equation by 3 to get x = 1140
he has 1140 miles remaining to get to the finish point.
he has already traveled 2 * 1140 + 80 = 2360 miles from the start point.
2360 + 1140 = 3500
numbers look good.
2460 is 80 more than twice 1140
twice 1140 = 2280
add 80 to get 2360.
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