4-26. Nina has some nickels and 9 pennies in her pocket. Her friend, Maurice, has
twice as many nickels as Nina. Together, these coins are worth 84¢. How many
nickels does Nina have? Show all of your work and label your answers.
Let n = # of nickels Nina has
m = # of nickels Maurice has
Nina has some nickels and 9 pennies  5n + 9 tells how much money Nina has
Maurice has twice as many nickels as Nina  m = 2n
5m tells how much money Maurice has
There is 84¢ in total  5n + 9 + 5m = 84
Our two equations are:
m = 2n
5n + 9 + 5m = 84
We use substitution (because m = 2n) and get
Nina has 5 nickels.
5n + 9 + 5(2n) = 84
5n + 9 + 10n = 84
15n + 9 = 84
–9 –9
15n = 75
15
15
n=5
4-38. The Fabulous Footballers scored an incredible 55 points at last night's game.
Interestingly, the number of field goals was 1 more than twice the number of
touchdowns. The Fabulous Footballers earned 7 points for each touchdown and 3
points for each field goal.
a. Multiple Choice: Which system of equations below best represents this situation?
Explain your reasoning. Assume that t represents the number of touchdowns
and f represents the number of field goals.
ii
f = 2t + 1
[# field goals is one more than twice the # touchdowns]
7t + 3f = 55
[7 points for each touchdown and 3 for each field goal, 55 points total]
b. Solve the system you selected in part (a) and determine how many touchdowns
and field goals the Fabulous Footballers earned last night.
Using substitution because f = 2t + 1 and get
7t + 3(2t + 1) = 55
7t + 6t + 3 = 55
13t + 3 = 55
–3 –3
13t = 52
13
13
t =4
Now we substitute t = 4 into f = 2t + 1 and get
f = 2(4) + 1
f=8+1
f=9
The Fabulous Footballers scored 4 touchdowns and 9 field goals.
4-40. Kevin and his little sister, Katy, are trying to solve the system of equations
shown below. Kevin thinks the new equation should be 3(6x − 1) + 2y= 43, while
Katy thinks it should be 3x + 2(6x − 1) = 43. Who is correct and why?
Katy is correct because y = 6x – 1 so we have to substitute y = 6x – 1 in 3x + 2y = 43.
This means we replace y with 6x – 1 to get 3x + 2(6x – 1) = 43, which is what Katy
has.
4-51. Hotdogs and corndogs were sold at last night's football game. Use the
information below to write mathematical sentences to help you determine how many
corndogs were sold.
a. The number of hotdogs sold was three fewer than twice the number of
corndogs. Write a mathematical sentence that relates the number of hotdogs
and corndogs. Let h represent the number of hotdogs and c represent the
number of corndogs.
h = 2c – 3 [hotdogs is three fewer (–3) than twice the corndogs (2c)]
b. A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write a
mathematical sentence to represent this information.
3h + 1.5c = 201
c. How many corndogs were sold? Show how you found your answer.
Our two equations are:
h = 2c – 3
3h + 1.5c = 201
Using substitution because h = 2c – 3 we get: 3(2c – 3) + 1.5c = 201
6c – 9 + 1.5c = 201
1.5c – 9 = 201
+9
+9
1.5c = 210
1.5 1.5
c = 140
4-62. On Tuesday the cafeteria sold pizza slices and burritos. The number of pizza
slices sold was 20 less than twice the number of burritos sold. Pizza sold for $2.50 a
slice and burritos for $3.00 each. The cafeteria collected a total of $358 for selling
these two items.
a. Write two equations with two variables to represent the information in this
problem. Be sure to define your variables.
Let p = # pizza slices
b = # burritos
Pizza slices is 20 less (–20) than twice the burritos (2b)  p = 2b – 20
Pizza is 2.50 and burritos are 3.00 for a total of 358  2.5p + 3b = 358
b. Solve the system from part (a). Then determine how many pizza slices were
sold.
Using substitution because p = 2b – 20 we get:
2.5(2b – 20) + 3b = 358
5b – 50 + 3b = 358
8b – 50 = 358
+ 50 + 50
8b = 408
8 8
b = 51
Then substitute b = 51 into p = 2b – 20 we get:
p = 2(51) – 20
p = 105 – 20
p = 85
The cafeteria sold 85 pizza slices (and 51 burritos).