Let

J = number of times Jones carried the ball

S = number of times Smith carried the ball

J +S = 26 --------(i)

Jones gained 100 yards in J carries, so, 100/J = average number of yards per J.

Smith gained 80 yards in S carries, so, 80/S = average number of yards per S.

100/J = 2(80/S) ----(ii)

100/J = 160/S

Cross multiply,

100*S = 160*J

10S = 16J

5S = 8J --------(iia)

From (i), J = 26 -S

Substitute that into (iia),

5s = 8(26 -S)

5s = 8*26 -8S

5S +8S = 8*26

13S = 8*26

Divide both sides by 13,

S = 8*2

S = 16 carries ----------answer.