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 = 152F + _ + F + _ + A + _ + A + _ + A + _ + A + _ + A = 136 ------> 2F + 5A + 6 = 1363F + 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 long6F + 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 longHow 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 ambulancesAnswer: D.)- Algebra House
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