Gavin went on 25 runs last month that totaled 103 miles. Each run was a distance of either 3 miles or 5 miles. Which system of
equations can be used to determine the number of 3-mile runs, x, and the number of 5-mile runs, y, that Gavin went on last month?

3x+5y=105

x+y=25

Step-by-step explanation:

x is the number of 3 mile runs so the total distance travelled is 3x miles.  y is the number of 5 mile runs so the total distance travelled is 5y miles.  Together Gavin travelled 103 miles so 3x+5y=105.  

The number of 3 mile and 5 mile runs he did in total were 25 so x+y=25.  

So the answer is:

3x+5y=105

x+y=25

Done.  

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have