Question

Joe earns $14 an hour and Blaine earns $18 per hour. Joe receives a raise of $1.75 every six months, and Blaine receives a raise of $0.75 every six months. Write and solve an equation that can be used to find x, the number of six-month intervals it will take Joe to earn the same hourly rate as Blaine. (Show your work)

Answer 1

After 4 interval of six months, Joe to earn same hourly rate as Blaine

Solution:

Given that,

Amount earned by Joe = $ 14 per hour

Amount earned by Blaine = $ 18 per hour

Lets assume the number of six month intervals be "x"

Joe receives a raise of $1.75 every six months

Therefore,

Joe earning: 14 + 1.75(number of six month intervals)

Equation for Joe earning: 14 + 1.75x ------- eqn 1

Blaine receives a raise of $0.75 every six months

Therefore,

Blaine earning: 18 + 0.75(number of six month intervals)

Equation for Blaine earning: 18 + 0.75x ------------ eqn 2

The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,

Eqn 1 must be equal to eqn 2

$14+1.75x = 18+0.75x\\\\1.75x-0.75x = 18-14\\\\1x = 4\\\\x = 4$

Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.