A. Tell me if you want to know why
We need to do a system of equations here.
x + y = 275 (if you travel <em>x</em> km by bike and <em>y </em>km by bus, then you travel 275 km as given in the problem)
y = x + 55 (the problem stated that they were bussed (y) the amount they biked plus 55 more km (x + 55))
The second equation is already solved for y. So, we can plug it in to the first equation.
x + (x + 55) = 275
2x + 55 = 275 [combine x terms]
2x = 220 [subtract 55 from both sides]
x = 110 [divide by 2 to isolate x and solve for it]
Now we know that x is 110, the distance they traveled by bike.
And that's what we needed to answer the problem!
You can write a proportion because the two triangles are similar
= 
(the second fraction is longer because I added the full lengths of the larger triangle) cross multiply to get (x)(x + 1 + x - 2) = (x - 2)(x + x + 5)
which simplifies to (x)(2x - 1) = (x - 2)(2x + 5)
then 2x² - x = 2x² + 5x -4x - 10
then 2x² - x = 2x² + x - 10
then 2x² = 2x² + 2x - 10
subtract 2x² from both sides to get 0 = 2x - 10
add 10 to both sides to get 10 = 2x
divide both sides by 2 to get 5 = x
Answer:
Two to One
Step-by-step explanation:
