Question

The tables show the amount earned by James and Paco working at the same store.

What two equations can represent James and Paco's hourly wages, where h is the number of hours worked and d is the amount of money earned?

Compare the equations to determine if there is any difference between what James and Paco make each hour.

Answer 1

d(James) = 11.8h

d(Paco) = 12h

Paco makes $0.20/h more than James

Explanation:

equation: y = ax + b

James:

d(Amount of money earned) = ah(number of hours worked) + b

If James worked 3 hours: 3a + b = 35.4

If James worked 5 hours: 5a + b = 59

If

3a + b = 35.4

b = 35.4 - 3a

Then

5a + b = 59

5a + 35.4 - 3a = 59

2a = 59 - 35.4

2a = 23.6

a = 23.6/2

a = 11.8

If a = 11.8, then

3a + b = 35.4

3(11.8) + b = 35.4

35.4 + b = 35.4

b = 0

If a = 11.8 and b = 0

d(Amount of money earned) = ah(number of hours worked) + b

d = 11.8h

Each hour James works, he makes $11.8

Paco:

d(Amount of money earned) = ah(number of hours worked) + b

If Paco worked 2 hours: 2a + b = 24

If Paco worked 4 hours: 4a + b = 48

If

2a + b = 24

b = 24 - 2a

Then

4a + b = 48

4a + 24 - 2a = 48

2a = 48 - 24

2a = 24

a = 24/2

a = 12

If a = 12, then

2a + b = 24

2(12) + b = 24

24 + b = 24

b = 24 - 24

b = 0

If a = 12 and b = 0

d(Amount of money earned) = ah(number of hours worked) + b

d = 12h

Each hour Paco works, he makes $12

Answer 2

Explanation:

In order to determine if James and Paco earn different amounts of money per hour, you must find how much money they make in one hour.

James:

James makes $35.40 in 3 hours. So, in 1 hour, he would make 35.40/3 = 11.8.

James makes $11.80 an hour.

Therefore, his equation would be d = 11.8h

Paco:

Paco makes $24.00 in 2 hours. So, in 1 hour, he would make 24/2 = 12.

Paco makes $12.00 an hour.

Therefore, his equation would be d = 12h

Hence, Paco and James make different amounts of money. Paco makes 20 cents, or $0.20, more than James.