Download Word Problems in Standard Form.

Unit 3 - Linear Functions
Lesson #6
LINEAR WORD PROBLEMS IN STANDARD FORM
Sometimes there is no slope given or there appears to be 2 slopes! These two numbers are the number
per x and the number per y. Each of these is multiplied to x and y, respectively. There is no beginning
amount, nor are there points given. However, there may be a TOTAL involved. In this case, the
equation can be written in Ax  By  C form with C being the total amount. Neither variable is
dependent on the other in this case!
1. A 100-point test has x questions worth 2 points apiece and y questions worth 4 points apiece.
What is the total that is given? ____________________
What do the variables stand for:
x=____________________________, y= ____________________________
a. Write an equation that describes all possible numbers of questions that may be on the test.
b. If you have 24 questions worth 4 points apiece, how many questions will be worth 2 points apiece?
2. Louise has $36 in five-dollar bills and singles. How many of each type of bill does she have?
What is the total that is given? ____________________
What do the variables stand for:
x=____________________________, y= ____________________________
a. Write an equation.
b. If Louse has 2 five-dollar bills, how many singles does she have?
3. The Ramy family bought 4 sandwiches and 3 salads. They spent $24. Let x be the cost of a sandwich
and y be the cost of a salad.
What is the total that is given? ____________________
What do the variables stand for:
x=____________________________, y= ____________________________
a. Write an equation.
b. If each sandwich costs $3.75, how much did each salad cost?
WORD PROBLEMS OF ALL TYPES:
1. At age 12 Patrick weighed 43 kg; at age 14 he weighed 50 kg. Patrick’s age and weight are related.
Identify the variables in this situation: x= _________________ y= __________________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ Total: __________
one point 
,
,
 a second point: 

a. Find a linear equation relating Patrick’s weight to his age.
b. Use your equation to find out Patrick’s age when he weighed 38 kg.
2. The store at which Andy usually shops is having a sale. Roast beef costs $4 a pound and shrimp costs
$10 a pound.
Identify the variables in this situation: x= _________________ y= __________________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ Total: __________
one point 
,
,
 a second point: 

a. Write an equation to describe different possible combinations of Roast beef and shrimp that he can
buy for $96.
b) What is the greatest amount of shrimp he can buy?
3. Joshua started walking from his home at noon and 2 hours later he reached the park, which is 3 miles
away. His distance from home and the time he walks are related.
Identify the variables in this situation: x= _________________ y= __________________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ Total: __________
one point 
,
,
 a second point: 

a. Write an equation that relates time and distance from home, assuming Joshua’s speed is constant.
(hint: how far is Joshua from his home when he starts walking?)
b. If Joshua continues to walk at the same pace, how far from home will he be at 5 p.m.?
4. The size of shoe a person needs has a linear relationship to the length of his or her foot. An adult
shoe that is Size 5 fits a 9-inch long foot. An 11-inch foot requires a size 11 shoe.
Identify the variables in this situation: x= _________________ y= __________________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ Total: __________
one point 
,
,
 a second point: 

a. Write the equation that describes shoe size as a function of foot length.
b. Bob Lanier of the Detroit Pistons wore a Size 22 shoe. How long is his foot?
5. It will take 20 points to make the playoffs, the hockey team coach told the players. “We get 2 points
for a win and 1 point for a tie.” Let W be the number of wins and T the number of ties.
Identify the variables in this situation: x= _________________ y= __________________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ Total: __________
one point 
,
,
 a second point: 

a. Write an equation to describe the values of W and T that will let the team make the playoffs.
b. If the team wins 7 games, how many tie games will need to occur?