Am I solving price elasticity of demand correctly

Question

Quantity demand is given by the equation 50 - 10p + .5y where p is price and y is income.

Bob's income is $40,000.

Dylan's income is $80,000.

Both Bob and Dylan pay $2 as their price.

I'm asked to find the price elasticities for both Bob and Dylan, indicate whether they are elastic or inelastic, and compare whether Bob or Dylan has a more elastic demand.

My reasoning:

For Bob Quantity Demanded is 50 - 10(2) + .5(40,000) = 20,030

For Dylan Quantity Demanded is 50 - 10(2) + .5(80,000) = 40,030

Price Elasticity is percentage change in Quantity Demanded over percentage change in Price.

Choosing an arbitrary Price $4 I solve for Quantity Demanded for Bob and Dylan.

For Bob Quantity Demanded is 50 - 10(4) + .5(40,000) = 20,010

For Dylan Quantity Demanded is 50 - 10(4) + .5(80,000) = 40,010

For Bob's percentage change in Quantity Demanded: (20,010 - 20,030) / 100 = -.2 = 20%

For Bob's percentage change in Price: (4 - 2) / 2 = 1 = 100%

For Bob's price elasticity of demand: Absolute value of -20 / 100 = .2 which is less than 1 so is inelastic

For Dylan's percentage change in Quantity Demanded: (40,010 - 40,030) / 100 = -.2 = 20%

For Bob's percentage change in Price: (4 - 2) / 2 = 1 = 100%

For Bob's price elasticity of demand: Absolute value of -20 / 100 = .2 which is less than 1 so is inelastic.

I'm doubting my answer because Bob and Dylan have price elasticities which are both inelastic and neither has a more elastic demand than the other. Am I doing something wrong?

Answer 1

As comments have pointed out I was calculating percentage change incorrectly. it should be [(20,010 - 20,030) / 20,010 ] x 100.