In a ball game, two rushers, smith and jones carried the ball a total of 26 plays. Smith gained 80 yards and jones gained 100 yards. If jones averaged twice as many yards per carry as smith, then on how many times did smith carry the ball?
In a ball game, two rushers, smith and jones carried the ball a total of 26 plays. Smith gained 80 yards and jones gained 100 yards. If jones averaged twice as many yards per carry as smith, then on how many times did smith carry the ball?
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.