System of equations {ACT}

Three fire trucks and 4 ambulances can fit into a parking lane 152 ft long.  Two fire trucks and 5 ambulances can fit into a lane 136 ft long.  How many feet long must a parking lane be for 1 fire truck and 5 ambulances?  Assume
there is 1 ft of space between each vehicle.
A.)  75 ft
B.)  90 ft
C.)  100 ft
D.)  105 ft
E.)  110 ft

F = length of one fire truck
A = length of one ambulance

F + _ + F + _ + F + _ + A + _ + A + _ + A + _ + A = 152 ------> 3F + 4A + 6 = 152
F + _ + F + _ + A + _ + A + _ + A + _ + A + _ + A = 136 ------> 2F + 5A + 6 = 136

3F + 4A = 146   {subtracted 6 from each side in 1st equation}
2F + 5A = 130   {subtracted 6 from each side in 2nd equation}

-6F – 8A = -292   {multiplied 1st equation by -2}
6F + 15A = 390   {multiplied 2nd equation by 3}
           7A = 98   {added the two equations}
             A = 14    {divided each side by 7}
Ambulance is 14 ft long

6F + 15A = 390
6F + 15(14) = 390   {substituted 14 for A}
6F + 210 = 390   {multiplied 15 by 14}
6F = 180   {subtracted 210 from each side}
F = 30   {divided each side by 6}
Fire truck is 30 ft long

How many feet must a parking lane be for 1 fire truck and 5 ambulances?

1F + _ + A + _ + A + _ + A + _ + A + _ + A -----> F + 5A + 5 = ?
= 30 + 5(14) + 5   {substituted 30 for F and 14 for A}
= 30 + 70 + 5   {multiplied 5 by 14}
= 105 feet of parking space for 1 fire truck and 5 ambulances
Answer:  D.)

- Algebra House