Download Name: Date: Awesome Algebra!!! Solve the following word problems

Name: _______________________
Date: _______________________
Awesome Algebra!!!
Solve the following word problems. Be sure to show your work and remember,
WORK DOWN! This will be good practice for the quiz tomorrow and a nice
challenge. Feel free to draw pictures if that helps. Have fun!
1.) When 9 is subtracted from a number and then divided by 2, the answer is 4.
What is the number?
(X– 9) ÷ 2 = 4
(X – 9) = 4 x 2
(X – 9) = 8
X=8+9
X = 17
2.) The length of a rectangle is twice that of the width. The perimeter of the
rectangle is 24 cm. What is the width of the rectangle?
L = 2W

2(2W) +2W = 24
4W + 2W = 24
6W = 24
W = 24 ÷ 6
W=4
3.) Marcus, Sally and Sammy decided to share 20 sweets. Marcus took 8 sweets and
Sally took three times as many as Sammy. How many sweets did Sammy receive?
8 + 3X = 20
3X = 20 – 8
3X = 12
X = 12 ÷ 3
X=4
4.) If the sum of three consecutive numbers is 72, what is the largest number?
X + (X + 1) + (X + 2) = 72
3X + 3= 72
3X = 72 – 3
3X = 69
X = 69 ÷ 3
X = 23
 23, 24 and 25. The largest number is 25.
5.) Andy is 2 times younger than his sister and his father is 25 years older than him.
If the total of their ages is 53 years, what is Andy's age and his father's age?
Let Andy = x
Father = 25 + x
Sister = 2x

X + (X + 25) + 2X = 53
4X + 25 = 53
4X = 53 – 25
4X = 28
X = 28 ÷ 4
X=7
Andy is 7 and his father is 25 + 7 which is 32.
Challenge work
Carol is y years old and her daughter is 25 years younger. Find Carol’s present age if
the sum of their ages in 6 years time is 75 years.
Carol = Y
Daughter = Y – 25

Y + (Y – 25) = 75
2Y – 25 = 75
2Y = 75 + 25
2Y = 100
Y = 100 ÷ 2
Y = 50
Carol will be 50yrs old in 6 years and her daughter will be 50 – 25 or 25 yrs old.
Therefore, Carol’s current age is 50 – 6 which is 44 yrs old.
Diana buys 20 apples at x cents each and 40 oranges at x + 10 cents. She packs them
into bags containing 5 apples and 10 oranges and sells the bags for 20x cents each. .
Find out the amount that Diana paid for each apple if she obtained a total of $24
from selling all the fruits.