Over the weekend, mario bicycled 43 miles. on sunday he rode 3 miles more than two-thirds of his distance on saturday. find the number of miles he rode each day.

We can solve this by writing down all of the variables we know. We will call the distance traveled on Saturday, x. The distance traveled on Sunday will be y.

x = distance traveled saturday
y = distance traveled sunday

We are told that on sunday he rode 3 miles more than 2/3 the distance on saturday. We can write a new formula.

y = (2/3)x + 3

We also not the total distance travelled, x + y = 43, now we solve for x.

x + y = 43
x + (2/3)x + 3 = 43
5/3x = 40
x = 24 miles

y = (2/3)(24)+3
y = 19 miles

Therefore, Mario biked 24 miles on Saturday and 19 miles on Sunday which gives us the total of 43 miles for the whole weekend.