Consecutive
Find the smaller of 2 consecutive integers if the sum of the smaller and twice the larger is −4. Write an equation.
x + 2(x + 1) = -4
x + 2x + 2 = -4
3x + 2 = -4
x = -2
2 consecutive integers: -2, -1
Ans: smaller integer is -2
Twice the sum of a number and −6 is −6 . Find the number. Write an equation.
2(x - 6) = -6
2x - 12 = -6
x = 3
Ans: number is 3
Logan is 2 years older than Lindsey. Five years ago, the sum of their ages was 30. If L is Lindsey’s current age, find it. Write an equation.
Logan: L + 2 - 5
Lindsey: L - 5
(L - 5) + (L + 2 - 5) = 30
L = 19
Ans: Lindsey's age is 19 years old.
A car travelling at 60 mph leaves Ithaca and travels west. Two hours later, a truck travelling at 55 mph leaves Elmira and travels East. Altogether, the car and truck travel 407.5 miles. How many hours does the car travel? Write an equation.
d = rt
407.5 = car + truck
407.5 = 60t + 55(t - 2)
407.5 = 60t + 55t - 110
t = 4.5
Ans: The car traveled 4.5 hours.
The total charge for a taxi ride in NYC includes an initial fee of $3.75 plus $1.25 for every 1/2 mile traveled. Jodi took a taxi, and the ride cost her exactly $12.50. How many miles did she travel in the taxi? Write an equation.
initial fee + 1.25 per 1/2 mile = 12.50
3.75 + 2.50 per mile = 12.50
m = miles traveled
3.75 + 2.50m = 12.50
m = 3.5
Ans: Jodi traveled 3.5 miles.
The perimeter of a triangular garden with 3 equal sides is 12.66 feet. What is the length of each side of the garden? Write an equation.
s = side
3s = 12.66
s = 4.22
Ans: length of one side is 4.22 feet
Find the smaller of 2 consecutive even integers if the sum of twice the smaller integer and the larger integer is −16. Write an equation.
2 even integers: n, n + 2
2n + (n + 2) = -16
n = -6
2 even integers: -6, -4
Ans: -6
Twice the difference of a number and −3 is 4. Find the number. Write an equation.
n = number
2(n - (-3)) = 4
2(n + 3) = 4
n = -1
Ans: number is -1
Brooke is 3 years younger than Samantha. In 5 years, the sum of their ages will be 29. Find Brooke’s age. Write an equation.
Brooke: s - 3 +5
Samantha: s +5
Brooke + Samantha = 29
(s + 2) + (s + 5) = 29
2s + 7 = 29
s = 11
Ans: Samantha is 11, Brooke is 8
A car traveling at 70 miles per hour traveled one hour longer than a truck traveling at 60 miles per hour. If the car and truck traveled a total of 330 miles, for how many hours did the car and truck travel altogether? Write an equation.
d = rt
car + truck = total distance
70(t + 1) + 60t = 330
70t + 70 + 60t = 330
t = 2
car traveled 3 hours, truck traveled 2 hours
Ans: total 5 hours together
The Cozo family has 5 children. While on vacation, they went to a play. They bought 5 tickets at the child’s price of $10.25 and 2 tickets at the adult’s price. If they spent a total of $89.15, how much was the price of each adult ticket?
child ticket + adult ticket = total
a = adult ticket
5(10.25) + 2a = 89.15
a = 18.95
Ans: price of each adult ticket is $18.95.
The length of a rectangle is twice the width. If the perimeter of the rectangle is 30 units, find the area of the garden. Write an equation.
w = width
2w + w + 2w + w = 30
6w = 30
w = 5
width is 5 units, length is 10 units
Ans: area is 5 * 10 = 50 units squared
The ages of 3 brothers are represented by consecutive integers. If the oldest brother’s age is decreased by twice the youngest brother’s age, the result is −19. How old is the youngest brother? Write the equation.
consecutive integers: n, n + 1, n + 2
youngest: n
oldest: n + 2
oldest - 2*youngest = -19
(n + 2) - 2n = -19
-n + 2 = -19
n = 21
Ans: youngest is 21 years old
Jeff sold half of his baseball cards then bought 16 more. He now has 21 baseball cards. How many cards did he begin with? Write an equation.
c = cards to begin
1/2 c + 16 = 21
c = 10
Ans: He began with 10 cards.
During a recent sale, the first movie purchased cost $29, and each additional movie purchased costs 𝑚 dollars. If Jose buys 4 movies and spends a total of $64.80, how much did each additional movie cost? Write an equation.
first movie + additional movies = total
m = additional movie cost
29 + 3m = 64.80
m = 11.93
Ans: Each additional movie costs $11.93.
An apple has 80 calories. This is 12 less than 1/4
the number of calories in a package of candy. How many calories are in the candy? Write an equation.
c = candy calories
80 = 1/4 c - 12
c = 368
Ans: 368 calories
The Hipster Dance company purchases 5 bus tickets that cost $150 each, and they have 7 bags that cost 𝑏 dollars each. If the total bill is $823.50, how much does each bag cost? Write an equation.
5 bus tickets + 7 bags = total bill
5(150) + 7b = 823.50
750 + 7b = 823.50
b = 10.5
Ans: one bag costs $10.50
A carpenter uses 3 hinges on every door he hangs. He hangs 4 doors on the first floor and 𝑥 doors on the second floor. If he uses 36 hinges total, how many doors did he hang on the second floor? Write the equation.
3 hinges per door
x = second floor doors
3(first floor doors + second floor doors) = 36
3(4 + x) = 36
12 + 3x = 36
x = 8
Ans: 8 doors
Kate has 12 1/2 pounds of chocolate. She gives each of her 5 friends 𝑥 pounds each and has 3 1/3 pounds left over. How much did she give each of her friends? Write the equation.
5x + 3 1/3 = 12 1/2
x = 1 5/6
Ans: 1 5/6 pounds
A room is 20 feet long. If a couch that is 12 1/3 feet long is to be centered in the room, how big of a table can be placed on either side of the couch? Write an equation.
length of whole room = table + couch + table
t = length of table
20 = t + 12 1/3 + t
20 = 2t + 12 1/3
t = 3 5/6
Ans: 3 5/6 feet
The weekend before final exams, Travis studied 1.5 hours for his science exam, 2 1/4 hours for his math exam, and ℎ hours each for Spanish, English, and social studies. If he spent a total of 11 1/4 hours studying, how much time did he spend studying for Spanish? Write an equation.
science + math + spanish + english + social studies = total hours
1.5 + 2 1/4 + h + h + h = 11 1/4
1.5 + 2.25 + 3h = 11.25
h = 2.5
Ans: He studied for Spanish for 2.5 hours.