Standard and Benchmark Assessed:
Standard: Patterns, Functions and Algebra
Benchmark: D. Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
Multiple Choice Question:
26. For e ver y la wn that she mo ws, Ja ne ch a rg es $8 per hour f or ever y ho ur that she work s. For each la wn that he m o ws, Bo b charg es a f ixe d f ee of
$20 an d an a dd itio na l $5 f or ever y hour t hat he work s.
W hat is the f ewest n umber of hours that both cou ld work so that Jane’s total pay for a lawn will be greater than Bob’s?
A. 1 hour
B. 5 hours
C. 6 hours
D. 7 hours
Commentary:
This multiple-choice question asks students to model and compare a problem situation. After modeling the situation, the student compares the total payments of the two workers at their different pay rates. The student could solve this question by creating a table or writing and solving two functions algebraically or graphically.
A model function for Jane’s pay is
P = 8 H , where P is her pay and H the hours worked. A model function for Bob’s pay is B = 20 + 5 H , where B is his pay and H his hours worked. The question asks for the fewest hours worked where Jane’s pay is more than Bob’s pay. This leads to the inequality 8 H > 20+ 5 H , subtract 5 H
2 from each side, 3 H > 20, divide by 3 gives a solution of H > 6
3
. They would have to work more
2 than 6
3 hours for Jane to earn more. Choice D, 7 hours, is the correct answer. Choices A, B
2 and C are all less than 6
3
Using a table:
and Bob would earn more money than Jane for these hours worked.
Hours
Jane
Bob
1
8
25
2
16
30
3
24
35
4
32
40
5
40
45
6
48
50
7
56
55
8
64
60
This also displays that 7 hours is the fewest hours they can work where Jane will earn more money than Bob.
Source: Ohio Department of Education July 05

The level of complexity for this question is Moderate Complexity, as students are required to select and use a representation and use this representation to solve a word problem.
Performance Data:
The percent of public school students selecting answer choice D for question 26 on the March
2005 Ohio Graduation Test was 65%.
Key Words: representation, table, function, solve
Source: Ohio Department of Education July 05