Team A beat Team B by a score of 37-29. Points were scored off of Touchdowns (6points) extra points (1point) and field goals (3points). There were 4 more touchd

Question

I need help figuring how to set the equation properly and how to solve it completely. Any input helps

Answer 1

6T+E+3F = 37

with 0<E<4

could be 6 touchdowns, 1 extra point or

5 touchdowns 1 extra point & 2 field goals

could be 5 touchdowns, 4 extra points & 1 field goal

or other combinations

If just 4 touchdowns, again 4 extra points, & 3 field goals

E has to be 4 or less

for team B

6T +E+3F = 29

There's missing information to narrow down what happened. "There's 4 more touchdowns....." than what?

than field goals?

then for Team B, T=F+4

then T=4 with F=0 would give E=5 which is impossible as E<T

so F>0

T=4, F=1, then E= 4, but that's not possible as T=F+4

So "4 more touchdowns" than field goals can't be right, for Team B

Maybe it meant 4 more for A than B?

As a practical matter, that's unlikely, but possible. T<6 for A, so T<2 for B, meaning 12 points on touchdowns, leaving 29-12 = 17 points on field goals, with E<2, leaving 16 points on field goals. 15 is possible, 5 x 3 with F=5, E=2=T for B, and T=6, E=1, F=0 for A. A looks like the running passing team, and B the kicking team. IF so,

A got 6 touchdowns, but only 1 extra point and no field goals 6x6+1=37

B got 2 touchdowns, 2 extra points and 5 field goals: 2x6+2+5x3 = 12+2+15 = 29