Solve One Variable
2x - 12 = 8
x = 10
x - 6 = 3x + 4
x = -5
You bought a magazine for $3.25 and 3 candy bars.
You spent a total of $6.70.
How much did each candy bar cost?
3.25 + 3x = 6.70
x = 1.15
$1.15
I read 5 pages of my book every night. Sarah started on page 20 and reads 3 books every night. How many nights until we have read the same number of pages?
5x = 20 + 3x
x = 10
10 nights
3(x+1)
3x + 3
(1/2)x = 3
x = 6
4 - x = 14 + 5x
x = -5/3
Jill sold half her comic books and then bought 16 more.
She now has 36 comic books.
How many did she have to start?
x/2 + 16 = 36
x = 40
40 books
At a movie theater, a basic popcorn costs $6, plus $1 for each additional flavoring. At a different theater, the same popcorn costs $5, plus $1.50 for each additional flavoring. Write and solve an algebraic equation to determine the number of flavorings you would need to add so that the total cost is the same at both theaters.
6x + 1 = 5x + 1.50
x = 2
2 flavorings
-8x-6
-14x + 7 = -21
x = 2
4x + 3x - 1.15 = 1.65
0.4 = x
You ordered 2 fish sandwiches and a hamburger. The cost of the hamburger is $2.50. Your total bill is $14.30. Write and solve an equation to find the cost of a fish sandwich.
2x+2.50 = 14.30
x = 5.9
$5.90
Your and your friend each purchase an equal number c of candy bars. Your candy bars cost $1.75 each and your friend’s candy bars cost $1.45 each. The total cost for you and your friend is $12.80. Write and solve an equation to find the number of candy bars you purchased.
1.75c + 1.45c = 12.80
c = 4
We each bought 4
-1/2 (-4x + 5)
2x - 2.5 OR 2x - (5/2)
13(x - 5) = 13
x = 6
8(1 + 1/2x)=2(x + 3)
x = -1
The sum of three consecutive numbers is 93.
What number is the smallest of these numbers?
x + (x+1) + (x+2) = 93
x = 30
Smallest # is 30
At an amusement park, the entry fee for a go-kart ride is $4, plus $5 per lap. At another amusement park, the entry fee for a go-kart ride is $3.50, plus $6 per lap. Write and solve an algebraic equation to determine the number of laps you would need to drive so that the total cost is the same at both parks.
4 + 5x = 3.50 + 6x
x = 0.5
Half a lap
3/4 (5x - 4)
(15x/3) - 3 OR (15/3)x - 3
4 - x = -10
x = 14
5d - 11 = 2d + 2
x = 13/3
The cooking club made some pies to sell at a basketball game. The cafeteria contributed 4 pies to the sale. Each pie was then cut into five pieces and sold. There were 60 pieces of pie. How many pies did the club make?
5(x + 4) = 60
x = 8
8 pies
Two friends, Sarah and John, are comparing their savings accounts. Sarah starts with $100 in her account and saves $20 per week. John starts with $150 in his account but spends $10 per week. Write and solve an algebraic equation to determine how many weeks it will take for Sarah to have the same amount of money as John.
100 + 20x = 150 - 10x
x = 5/3
1 and 1/3 weeks
6 (2 + 1/2x)
12 +3x