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.