Answer to Question #265176 in Algebra for Leyla

Question

Nick works on a tree farm, bundling

seedlings. His workweek is 40 h, and he can

complete three bundles per hour. He needs

to choose one of the following rates of pay:

i) $8.75 per hour

ii) $4.75 per hour plus $1.35 per bundle

iii) $2.75 per bundle

a) Write an algebraic expression that

shows Nick’s weekly earnings at each

rate of pay.

b) Which rate of pay should Nick choose?

Use your algebraic expressions to

support your answer.

Answer 1

Solution:

a)

i) Algebraic equation for the first rate ($8.75 per hour):

y = 8.75t, where t is time

ii) Algebraic equation for the second rate ( $4.75 per hour plus $1.35 per bundle ):

y = 4.75t + 3 * 1.35t

y = 4.75t + 4.05t

y = 8.80t, where t is time

iii) Algebraic equation for the third rate ($2.75 per bundle):

y = 3 * 2.75t

y = 8.25t

b)

When t (time) = 40 hours

i) y = 8.75 * 40

y = 350

So when Nick works 40 hours/week, his salary with the first type of rate will be $350

ii) y = 8.80 * 40

y = 352

So when Nick works 40 hours/week, his salary with the second type of rate will be $352

iii) y = 8.25 * 40

y = 330

So when Nick works 40 hours/week, his salary with the third type of rate will be $330

As we can see the most profitable rate is the 2nd rate ($4.75 per hour plus $1.35 per bundle), where he can earn $352.