1. # of hot dogs Money from hot dogs # of drinks Money from drinks
Do you remember this problem, and how we solved it?
Harry and Joan sold hot dogs and drinks outside on a nice summer day. The hot dogs cost $1.00 each, and the drinks cost $0.50 each. They sold a total of 30 items (hot dogs and drinks) and took in $19. How many hot dogs and drinks did they sell?
# of hot dogs
Money from hot dogs
# of drinks
Money from drinks
Total Items
Total Money 1
1.00 29
14.50 30
15.50 2
2.00 28
14.00
16.00 3
3.00 27
13.50
16.50 4
4.00 26
13.00
17.00 6
6.00 24
12.00
18.00 8
8.00 22
11.00
19.00
Sometimes it is difficult to write your own equations from a word problem. It helps some students if they take the information from a paragraph, and place facts into a table. The headings on the rows and columns may change for each problem, but the process stays pretty much the same. You will still need to show all of your work. The table just helps you organize yourself.

2. Number sold Cost of one Total spent Hot dogs Soda Total
Do you remember this problem? Let’s solve it a new way.
Harry and Joan sold hot dogs and drinks outside on a nice summer day. The hot dogs cost $1.00 each, and the drinks cost $0.50 each. They sold a total of 30 items (hot dogs and drinks) and took in $19. How many hot dogs and drinks did they sell?
Can you write the equations that can be made from the facts of this problem?
Do you know how many hot dogs were sold? Can you use a number for it or do you need to use a variable?
Do you know how many drinks were sold? Can you use a number for it or do you need to use a variable?
Do you know how many items were sold? Can you use a number for it or do you need to use a variable expression?
How do you get the amount of money spent on all everything purchased? Can you use a number for it or do you need to use a variable expression?
How do you get the amount of money spent on the hot dogs? Can you use a number for it or do you need to use a variable expression?
How do you get the amount of money spent on the drinks? Can you use a number for it or do you need to use a variable expression?
Number sold
Cost of one
Total spent
Hot dogs
Soda
Total

3. Number sold Cost of one Total spent Hot dogs Drinks Total
Do you remember this problem? Let’s solve it a new way.
Harry and Joan sold hot dogs and drinks outside on a nice summer day. The hot dogs cost $1.00 each, and the drinks cost $0.50 each. They sold a total of 30 items (hot dogs and drinks) and took in $19. How many hot dogs and drinks did they sell?
Can you write the equations that can be made from the facts of this problem?
Do you know how many hot dogs were sold? Can you use a number for it or do you need to use a variable? You can use the variable h.
Do you know how many drinks were sold? Can you use a number for it or do you need to use a variable? You can use the variable d.
Do you know how many items were sold? Can you use a number for it or do you need to use a variable expression? There were 30 things sold. It is the sum of hot dogs & drinks.
How do you get the amount of money spent on all everything purchased? Can you use a number for it or do you need to use a variable expression? It cost $19 for all of the hot dogs and drinks.
How do you get the amount of money spent on the hot dogs? Can you use a number for it or do you need to use a variable expression? You multiply the number of dogs by one dollar.
How do you get the amount of money spent on the drinks? Can you use a number for it or do you need to use a variable expression? You multiply the number of drinks by fifty cents.
Number sold
Cost of one
Total spent
Hot dogs h
1.00
1.00h
Drinks d
0.50
0. 50d
Total 30
1.00h d = 19

4. h + d = 30 1.00h + 0.50d = 19 Number sold Cost of one Total spent
Do you remember this problem? Let’s solve it a new way.
Harry and Joan sold hot dogs and drinks outside on a nice summer day. The hot dogs cost $1.00 each, and the drinks cost $0.50 each. They sold a total of 30 items (hot dogs and drinks) and took in $19. How many hot dogs and drinks did they sell?
Can you write the equations that can be made from the facts of this problem?
To get the 30 items sold, you would add the number of hot dogs sold to the number of drinks sold.
h + d = 30
To get the $19 final cost, you would add the cost of the hot dogs to the cost of the drinks.
1.00h d = 19
Number sold
Cost of one
Total spent
Hot dogs h
1.00
1.00h
Drinks d
0.50
0. 50d
Total 30
1.00h d = 19

5. Try to fill in the chart with facts from the word problems.

6. Number sold Cost of one Total spent Hot dogs Soda Total
1. A group was selling hot dogs and soda before a game. Hot dogs cost $1.50 and sodas cost $0.75.At the end of an hour, they sold 15 items and collected $18. How many hot dogs and sodas did they sell?
Number sold
Cost of one
Total spent
Hot dogs
Soda
Total

7. Number sold Cost of one Total spent Hot dogs Soda Total
1. A group was selling hot dogs and soda before a game. Hot dogs cost $1.50 and sodas cost $0.75.At the end of an hour, they sold 15 items and collected $18. How many hot dogs and sodas did they sell?
Number sold
Cost of one
Total spent
Hot dogs h
1.50
1.50h
Soda s
0.75
0.75s
Total 15
1.50h s = 18
h + s = 15
1.50h s = 18
Solve for one of your variables to use when you substitute.
h = 15 - s
Substitute that into the other equation.
1.50 (15-s) s = 18
Solve for one of your variables to get an actual number.
22.50 – 1.50s s = 18
22.50 – 0.75s = 18
-0.75s = -4.50
÷ ÷ -0.75
s = 6
Plug that value in to the other equation to find the value of the other variable.
h + s = 15
h + 6 = 15
h = 9
Prove your answer works by plugging the values into both equations.

8. 2. You and a friend went to Taco Bell for lunch
2. You and a friend went to Taco Bell for lunch. You ordered 3 soft tacos and 3 burritos for $ Your friend ordered 4 soft tacos and 2 burritos for $10. How much do soft tacos cost? How much do burritos cost?
Number sold
Cost of one
Total spent
Soft Tacos
Burritos
Total

9. Solve for one of your variables to use when you substitute. b = 5 – 2t
2. You and a friend went to Taco Bell for lunch. You ordered 3 soft tacos and 3 burritos for $ Your friend ordered 4 soft tacos and 2 burritos for $10. How much do soft tacos cost? How much do burritos cost?
Number sold
Cost of one
Total spent
Soft Tacos 3 t 3t 4 4t
Burritos b 3b 2 2b
Total 6
3t + 3b = 11.25
4t + 2b = 10
3t + 3b = 11.25
4t + 2b = 10
Solve for one of your variables to use when you substitute.
b = 5 – 2t
Substitute that into the other equation.
3t + 3(5-2t) = 11.25
Solve for one of your variables to get an actual number.
3t + 15 – 6t = 11.25
15 – 3t = 11.25
-3t = -3.75
÷ ÷ -3
t = 1.25
Plug that value in to the other equation to find the value of the other variable.
4t+ 2b = 10
4 (1.25)+ 2b = 10
5 + 2b = 10
2b = 5
b = 2.50
Prove your answer works by plugging the values into both equations.

10. Number sold Cost of one Total spent Adult’s Children’s Total
3. Mr. Smith bought 7 tickets to a puppet show and spent a total of $43. Adult tickets cost $9 and children tickets cost $4. How many tickets of each type did Mr. Smith purchase?
Number sold
Cost of one
Total spent
Adult’s
Children’s
Total

11. Number sold Cost of one Total spent Adult’s Children’s Total
3. Mr. Smith bought 7 tickets to a puppet show and spent a total of $43. Adult tickets cost $9 and children tickets cost $4. How many tickets of each type did Mr. Smith purchase?
Number sold
Cost of one
Total spent
Adult’s a 9 9a
Children’s c 4 4c
Total 7
9a + 4c = 43
a + c = 7
9a + 4c = 43
Solve for one of your variables to use when you substitute.
a = 7 - c
Substitute that into the other equation.
9 (7-c) + 4c = 43
Solve for one of your variables to get an actual number.
63 – 9c + 4c = 43
63 – 5c = 43
-5c = -20
÷ ÷ -5
c= 4
Plug that value in to the other equation to find the value of the other variable.
a + c = 7
a + 4 = 7
a= 3
Prove your answer works by plugging the values into both equations.

12. Number sold Cost of one Total spent Adult’s Student’s Total
4. Sharon sold 461 tickets for a school play. Student tickets cost $3 and adult tickets cost $4. Sharon's sales totaled $1624. How many adult tickets and how many student tickets did Sharon sell?
Number sold
Cost of one
Total spent
Adult’s
Student’s
Total

13. Number sold Cost of one Total spent Adult’s Student’s Total
4. Sharon sold 461 tickets for a school play. Student tickets cost $3 and adult tickets cost $4. Sharon's sales totaled $1624. How many adult tickets and how many student tickets did Sharon sell?
Number sold
Cost of one
Total spent
Adult’s a 4 4a
Student’s s 3 3s
Total
461
4a + 3s = 1624
a + s = 461
4a + 3s = 1624
Solve for one of your variables to use when you substitute.
a = s
Substitute that into the other equation.
4 (461 - s) + 3s = 1624
Solve for one of your variables to get an actual number.
1844 – 4s + 3s = 1624
1844 – 1s = 1624
-1s = -220
÷ ÷ -1
s = 220
Plug that value in to the other equation to find the value of the other variable.
a + s = 461
a = 461
a = 241
Prove your answer works by plugging the values into both equations.

14. Number Larger Smaller Sum
5. Find two numbers that have a sum of 33 and a difference of 13.
Number
Larger
Smaller
Sum
Difference

15. Number Larger Smaller Sum
5. Find two numbers that have a sum of 33 and a difference of 13.
Number
Larger L
Smaller s
Sum 33
Difference 13
L + s = 33
L - s = 13
Solve for one of your variables to use when you substitute.
L = 33 - s
Substitute that into the other equation.
33 - s - s = 13
Solve for one of your variables to get an actual number.
33 – 2s = 13
-2s = -20
÷ ÷ -2
s = 10
Plug that value in to the other equation to find the value of the other variable.
L + s = 33
L + 10 = 33
L = 23
Prove your answer works by plugging the values into both equations.