求助,prep破解math

cougarhui

At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000.  Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.  If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?

 

(A) $10,000

(B) $11,200

(C) $12,000

(D) $12,800

(E) $13,200

我怎么算出来和选项没一个一样的啊

(50000+50000*0.2*0.4)-2*(20000+20000*0.2*0.4)=10800

答案是E，请有好心的NN帮忙解释下

izumichen

the finance charge is on the remainder of the cost, not on the downpayment of the cost as suggested by your answer

50000*0.2+50000*0.8*1.4- (40000*0.2+40000*0.8*1.4)

= 50000*(0.2+1.12)-40000*(0.2+1.12)

= (50000-40000)*1.32

= 13200

cougarhui

谢谢mm，原来我把先付和后付的搞反了

neomatrix

"making 20 percent down payment", it means that the purchaser of 2 A's will pay for

the remainder & finance charges for purchasing A & B respectively are:
A: 2*20000*0.8*1.4
B: 1*50000*0.8*1.4

here, buying A can pay 0.8*1.4*(50000-40000)=11200 less than B.

go back to the down payment, A costs 20%*(50000-40000)=2000 less than B.

Then, buying 2 A's will cost 11200+2000=13200 less than B.