Solving with Fractions
Multi-Step Equations
Word Problems -
2-step Equations
On Both Sides
Word Problems-
On Both Side
100
p + 1/10 = -3/4
p = -17/20
100
35 = 7(m + 7)
m = -2
100
Mr. Vargas takes his class of 24 students ice skating. Each student pays an entrance fee to enter the rink and a $4 fee to rent skates. The total cost for the student to enter the rink and rent skates is $216. Write and solve an equation to find the ice-skating rink's entrance fee.
24(x + 4) = 216 x = $5
100
p − 1 = 5p + 3p − 8
p = 1
100
Ashley went to the mall and bought a pair of jeans for $38, a sweatshirt for $25 and 3 makeup items from Sephora. Erin didn't buy any clothing, but she did purchase 6 items from Sephora. All the makeup items cost the same amount, and both girls spent the same amount of money. Write and solve an equation to find the cost of one makeup item.
38 + 25 + 3m = 6m m = $21
200
d - 4/9 = -1/12
d = 13/36
200
15 = 3/8(x - 5)
x = 45
200
Vanessa makes seven identical flower arrangements for the tables at a banquet. Each arrangement contains some roses and nine tulips. Vanessa uses a total of 147 flowers to make the arrangements. Write and solve an equation to find how many roses are in each arrangement.
7(r + 9) = 147 12 roses
200
5p − 14 = 8 p + 4
p = -6
200
Bill and Phil need to gain weight for the wrestling team. Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil? Write an equation and solve.
120 + 10m = 150 + 4m m = 5 months
300
-0.7 = -7/9x
x = 0.9 OR 9/10
300
3(p - 1.5) = 13.5
p = 6
300
Brody drives the same distance to and from work each day. He also drives an additional 1.5 miles each day to go to the gym. During a 5-day work week, Brody drives a total of 71.25 miles. Write and solve an equation to find the distance to and from work.
5(d + 1.5) = 71.25 d = 12.75 miles (6.375 each way)
300
5n + 34 = −2(1 − 7n)
n = 4
300
A twelve inch candle and an eighteen inch candle are lit at 6pm. The twelve inch candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours. Write an equation and solve.
12 - 0.5h = 18 - 2h h = 4 hours
400
5/2x+3=1/2x+15
x=6
400
-1/3(p + 1) = 1/6
p = -3/2
400
Maria and four of her friends all have discount passes to a movie theater. The passes are good for $2.95 off the regular price of admission. The 5 friends go to the theater together and spend a total of $47.75 on admission. Write and solve an equation to find the regular price of admission.
5(a - 2.95) = 47.75 a = $12.50
400
2(x - 4) + 8 = 3x - 8
x = 8
400
The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Spotify, you must be a member. The Spotify membership fee is $10. In addition, each purchased song costs $0.89. How many downloaded songs, d, must be purchased for the monthly price of Spotify to be the same as iTunes? Write an equation and solve.
0.99d = 10 + 0.89d d = 100 songs
500
3/7c+11=1/2c+13
c = -28
500
4/5(2 + m) = 24
m = 28
500
An airplane has two sections, business and economy class. In each section, there are six seats in a row. There are 24 rows in economy class, and there are 174 seats on the plane. Write and solve an equation to find how many rows of seats are there in business class.
6(b + 24) = 174 b = 5 rows
500
3n − 5 = −8(6 + 5n)
n = -1
500
Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water? Write an equation and solve.
800 - 6m = 1000 - 10m m = 50 minutes
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