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loan math problem
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lachlan has $600 cash and a car worth $500. that's $1,100. the new car is priced at $21,800. lachlan needs a loan for $20,700. however, the finance company insists that the buyer must pay a 10% deposit, which is $2,180. lachlan only has $1,100, so no loan.  the car dealer wants to make a sale, so suggests some tricks. the car dealer could buy lachlan's old banger for $1,500 instead of $500, and sell the new car for $22,800 instead of $21,800. doesn't make a difference to the dealer, he gets the same amount of cash. now lachlan has $600 cash and $1,500 for his car or $2,100 in total. he needs 10% of $22,800 as deposit which is $2,280. that's not quite there but you see how the principle works. lachlan is about $200 short. so the dealer adds $1,200 to both car prices. lachlan has $600 cash and a car "worth" $1,700, total $2,300. the new car is sold for $23,000 requiring a $2,300 deposit which works out exactly.  how could we have found the right amount without guessing?  lachlan had $1,100. the new car costs $21,800. the dealer increases both prices by x dollars. lachlan has now $1,100 + x deposit. the car now costs $21,800 + x. the deposit should be 10%, so $1,100 + x = 10% of ($21,800 + x) = $2,180 + 0.1 x.  $1,100 + x = $2,180 + 0.1 x : subtract $1,100 x = $1,080 + 0.1 x : subtract 0.1 x 0.9 x = $1,080 : divide by 0.9 x = $1,080 / 0.9 = $1,200 the dealer inflates the cost of the new car and the value of the old car by $1,200. now that's the theory. in practice i don't know how the finance company feels about this, and if they would be happy if they found out.
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