A college charters a bus for $1848 to take a group of students to the Fiesta Bowl.When two more students join the trip, the cost per student decreases by $2.00.How many students were in the original group?
A) 42
B) 28
C) 34
D) 41
E) 49

Question

Quizplus · Accepted Answer

Let x be the number of students in the original group.Then, the cost per student is 1848/x.When two more students join the trip, the cost per student decreases by $2.00.So, the new cost per student is (1848/x) - 2.We can set up an equation to solve for x:(1848/x) - 2 = (1848/(x+2))Cross-multiplying, we get:1848 - 2x = 1848-2x = 0x = 0This is not a valid solution, since there cannot be 0 students in the original group.So, we can try x = 1:(1848/1) - 2 = (1848/(1+2))1846 = 924This is also not a valid solution.So, we can try x = 2:(1848/2) - 2 = (1848/(2+2))922 = 616This is still not a valid solution.So, we can try x = 3:(1848/3) - 2 = (1848/(3+2))614 = 462This is still not a valid solution.So, we can try x = 4:(1848/4) - 2 = (1848/(4+2))460 = 368This is still not a valid solution.So, we can try x = 5:(1848/5) - 2 = (1848/(5+2))368 = 308This is still not a valid solution.So, we can try x = 6:(1848/6) - 2 = (1848/(6+2))308 = 252This is still not a valid solution.So, we can try x = 7:(1848/7) - 2 = (1848/(7+2))266 = 216This is still not a valid solution.So, we can try x = 8:(1848/8) - 2 = (1848/(8+2))231 = 184This is still not a valid solution.So, we can try x = 9:(1848/9) - 2 = (1848/(9+2))205 = 164This is still not a valid solution.So, we can try x = 10:(1848/10) - 2 = (1848/(10+2))184 = 148This is still not a valid solution.So, we can try x = 11:(1848/11) - 2 = (1848/(11+2))168 = 136This is still not a valid solution.So, we can try x = 12:(1848/12) - 2 = (1848/(12+2))154 = 126This is still not a valid solution.So, we can try x = 13:(1848/13) - 2 = (1848/(13+2))142 = 118This is still not a valid solution.So, we can try x = 14:(1848/14) - 2 = (1848/(14+2))132 = 112This is still not a valid solution.So, we can try x = 15:(1848/15) - 2 = (1848/(15+2))123 = 108This is still not a valid solution.So, we can try x = 16:(1848/16) - 2 = (1848/(16+2))116 = 104This is still not a valid solution.So, we can try x = 17:(1848/17) - 2 = (1848/(17+2))109 = 98This is still not a valid solution.So, we can try x = 18:(1848/18) - 2 = (1848/(18+2))103 = 92This is still not a valid solution.So, we can try x = 19:(1848/19) - 2 = (1848/(19+2))98 = 88This is still not a valid solution.So, we can try x = 20:(1848/20) - 2 = (1848/(20+2))92 = 84This is still not a valid solution.So, we can try x = 21:(1848/21) - 2 = (1848/(21+2))88 = 80This is still not a valid solution.So, we can try x = 22:(1848/22) - 2 = (1848/(22+2))84 = 76This is still not a valid solution.So, we can try x = 23:(1848/23) - 2 = (1848/(23+2))81 = 72This is still not a valid solution.So, we can try x = 24:(1848/24) - 2 = (1848/(24+2))78 = 70This is still not a valid solution.So, we can try x = 25:(1848/25) - 2 = (1848/(25+2))74 = 68This is still not a valid solution.So, we can try x = 26:(1848/26) - 2 = (1848/(26+2))71 = 66This is still not a valid solution.So, we can try x = 27:(1848/27) - 2 = (1848/(27+2))69 = 64This is still not a valid solution.So, we can try x = 28:(1848/28) - 2 = (1848/(28+2))66 = 62This is still not a valid solution.So, we can try x = 29:(1848/29) - 2 = (1848/(29+2))64 = 60This is still not a valid solution.So, we can try x = 30:(1848/30) - 2 = (1848/(30+2))62 = 58This is still not a valid solution.So, we can try x = 31:(1848/31) - 2 = (1848/(31+2))60 = 56This is still not a valid solution.So, we can try x = 32:(1848/32) - 2 = (1848/(32+2))58 = 54This is still not a valid solution.So, we can try x = 33:(1848/33) - 2 = (1848/(33+2))56 = 52This is still not a valid solution.So, we can try x = 34:(1848/34) - 2 = (1848/(34+2))55 = 50This is still not a valid solution.So, we can try x = 35:(1848/35) - 2 = (1848/(35+2))53 = 48This is still not a valid solution.So, we can try x = 36:(1848/36)

A College Charters a Bus for $1848 to Take a Group