Question #c6d42

1 Answer
Dec 12, 2015

Dory biked 143 miles last month.

Explanation:

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.