Question #c6d42

To find out how many miles Dory biked, you will first set up a system of equations with the data you have.

So since Dory biked 11 times as much as Karly, you could say that #D=11K# in which the #D# represents the number of miles Dory biked and the #K# represents the number of miles Karly biked.

So #D=11K# is our first equation.

We can find the other one from the other information given. Since they biked 156 miles together, we could say that #D+K=156#

So now that we have our equations, we can set them up so that we can eliminate one variable and keep the other one.

#D+K=156#
#D=11K#

But we need the #11K# on the same side of the equal sign as the #D#, so we can write it like this: #D-11K=0#. We do this by subtracting the #11K# from both sides.

So now we have:

#D+K=156#
#D-11K=0#

Now we can subtract the top equation from the bottom one, so #D-D# makes both of those disappear.
#+K- -11K#. Negative minus a negative is plus a positive so that #=12K#
And #156-0=156#

So our new equation is #12K=156#

We divide both sides by 12 to get #K=13#. So this means Karly biked 13 miles in the past month, but that's not what we need to answer the question, we need toknow how much Dory biked. So we can put the 13 in for #K# into one of our other equations to find #D#.

#D+13=156#

To solve this we simply subtract 13 from both sides.

#156-13=143# so #D=143#

So Dory biked 143 miles last month.
And we can even check this with the other equation #D=11K#. Does #143=11(13)#?
#11*13=143#, so yes.

So Dory biked 143 miles and Karly biked 13 miles last month.