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4.5C Notes - LINEAR WORD PROBLEMS (Standard Form & Slope Intercept 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 do the variables stand for:
x=______________________, y= ____________________ What is the total? ______________
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 do the variables stand for:
x=________________________, y= ______________________ What’s the total? ______________
a. Write an equation.
b. If Louise 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 do the variables stand for:
x=__________________________, y= ______________________ What is the total? ______________
a. Write an equation.
b. If each sandwich costs $3.75, how much did each salad cost?
Continued on back
4. A baby weighs 14 pounds at 5 months and 21 pounds at 10 months.
a. Write an equation in slope-intercept form that relates the baby’s weight, y, to the baby’s age, x.
b. Use your equation to find how much the baby weighed at birth.
c. How many pounds did the baby gain each month after in its first year?
CW: 4.5C Classwork (handout)
NAME: ______________________________________________ TABLE# ___ PER ___ DATE _______
4.5C CW (WORD PROBLEMS IN STANDARD FORM AND SLOPE INTERCEPT FORM)
For each word problem below, write a linear equation in standard form (Ax + By = C) or slope-intercept
form (y = mx + b). Then answer the additional questions.
1. You are in charge of buying food for your family reunion. You spend $90 on hamburgers and
turkey burgers. You pay $1.50 for each hamburger and $2 for each turkey burger. Let x be the
number of hamburgers and y be the number of turkey burgers.
a. Write an equation in standard form that represents the situation.
b. If you bought 30 turkey burgers, how many hamburgers did you buy?
2. You are selling drinks at the carnival to raise money for your club. You sell lemonade for $2 per
cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of
lemonade and y be the number of orange drinks.
a. Write an equation in standard form that represents the situation.
b. If you sold 60 cups of lemonade, how many cups of orange drink did you sell?
3. A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs.
Let x be the calf’s age and y be the weight.
a. Write an equation in slope-intercept form that represents the situation.
b. How much did the calf weigh at birth?
c. Approximately how much will the calf weigh when it is 12 months old?
d. How much weight did the calf gain each month?
4. A weightlifter uses 45 pound plates and 10 pound plates to lift 260 pounds. Let x represent the
number of 45 pound weights and y represent the number of 10 pound weights.
a. Write an equation in standard form the represents the situation.
b. If the weightlifter uses eight 10-pound weights, how many 45 pound weights did he use?
5. A taxi ride in Detroit costs $11 for 2 miles and $18 for 4 miles. Let x be the number of miles
and y be the total fare.
a. Write an equation in slope intercept form that represents the situation.
b. What is the initial fee?
c. What is the price per mile?
d. How much would it cost to take the same taxi for 10 miles?
6. You have $.80 in your backpack in dimes and quarters. Let x represent the number of dimes
and y represent the number of quarters.
a. Write an equation in standard form that represents the situation.
b. If you have 2 quarters in your backpack, how many dimes do you have?