i need answers to this. Help is needed.

Question

Cora ran 5 miles last month and will run ½ miles per week from now on. Hana ran 3 miles last month and will run ¾ miles per week from now on.



The following system of linear equations can be used to represent this situation, where y represents the total number of miles ran and x represents the number of weeks.

y=12x+5

y=34x+3

Determine how many weeks Cora and Hana must run in order for their total number of miles ran to be the same. Find the solution by graphing.

Cora and Hana must run for _______ weeks in order for their total mileage, _______ miles, to be the same.

Answer 1

If a = b and a = c, then b = c, right?

(1/2)x + 5 = (3/4)x + 3

(-1/4)x = -2

x = 8 weeks

(1/2)(8) + 5 = 9 miles

Fill in the blanks.

Answer 2

The equations should really be

y=1/2x+5

y=3/4x+3

Just set the two equations equal to each other and solve for x

x = 8

y = 9

They must run for 8 weeks for their total mileage to be 9 miles.

If you plot the two lines, the intersection point is at (8,9)