Word Problems
Clara sold half of her comic books and then bought 6 more. She now has 15. How many did she begin with?
1/2b+6=15
18 comic books
Solve for t.
d/t=r
t=d/r
What does vertical angles mean?
Angles are equal.
Solve for y.
-4(y – 2) + 9y = 3
y = -1
Define:
complementary angles
complement of an angle
supplementary angles
supplement of an angle
complementary: angles sum to 90
complement of an angle: 90 - x
supplementary angles: angles sum to 180
supplement of an angle: 180 - x
Oceanside Bike Rental Shop charges 14 dollars plus 6 dollars an hour for renting a bike. Alex paid 44 dollars to rent a bike. How many hours did she pay to have the bike checked out?
14+6h=44
5 hours
Solve for h.
A=1/2bh
h=(2A)/b
Solve for x.
7(x + 2) = -4x + 25
x = 1
Solve for the absolute value of n.
16 + 2n – 5 - 8n = 65
n = -9
Answer: |-9| = 9
x+4x=180
x = 36 degrees
other angle: 36*4 = 144 degrees
Mike had 258 dollars to spend on 9 books. After buying them he had 15 dollars. How much did each book cost?
9b+15=258
OR
9b=258-15
27 dollars
Solve for t.
A=P(1+rt)
t=(A-P)/(Pr)
Sam is ordering shirts online. The shipping is a flat rate of $5.99, and each shirt costs $12.50. He spent $80.99 in total. How many shirts did he order? Set up the equation only.
5.99+12.50x=80.99
Solve for m.
-7(m - 3) = 35 - 5m
m = -7
Two angles are vertical angles. One of the angles measures half the other, increased by 5. What are the angles?
x=1/2x+5
x = 10 degrees
Both equal 10 degrees.
The sum of three consecutive ODD numbers is 171. What is the equation AND the largest odd number?
x+(x+2)+(x+4)=171
55, 57, and 59 is the largest
Solve for a.
u+ka=ba
a=u/(b-k)
The sum of two consecutive numbers is 45. What is the equation and what are the two numbers?
x+(x+1)=45
22, 23
Solve for x.
5(x + 16) = -3(x + 8)
x = -13
12 less than twice the supplement of an angle is 2. What is the angle?
2(180-x)-12=2
x = 173 degrees
The sum of three consecutive EVEN numbers is -120. What is the smallest of the three numbers?
x+(x+2)+(x+4)=-120
-38, -40, and -42 is the smallest
Solve for a. (Hint: Cross Product Property)
g=(1+2a)/a
a=1/(g-2)
The length of a rectangle is 9 more than its width. Write and solve an equation to find the width AND length of the rectangle if its perimeter is 38 inches.
2w+2(w+9)=38
width is 5 inches
length is 14 inches
Solve for x.
3(x – 1) + 2(2x – 1) = 5(x – 2) + 2x + 5
7x - 5 = 7x - 5
Infinitely many solutions.
Half of the complement of an angle is four times the angle. What is the angle?
1/2(90-x)=4x
x = 10 degrees