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Math! Al From Gebra! Some Last Practice
Before Wednesday’s Quiz-Quiz
Solve all the following showing your steps! Enjoy as much as possible.
1. When a number is doubled, the result is forty-three.
2 x  43
2 x 43

2
2
x  21.5
Therefore, the number is 21.5!
2. Felix is twenty-nine years older than his daughter. Together, their ages are fifty-one.
Find the ages.
x  29  x  51
2 x  29  51
2 x  51  29
2 x  22
2 x 22

2
2
x  11
Therefore, the daughter is 11 and Felix is 11+29=40
3. The sum of three consecutive numbers is seventy-two. Find the numbers.
x  x  1  x  2  72
3 x  3  72
3 x  72  3
3 x  69
3 x 69

3
3
x  23
Therefore, the numbers are 23, 24, and 25.
4. When a number is subtracted from fifty-thousand, the result is sixty. Find the silly
number.
50000  x  60
50000  60  x  60  60
49940  x  0
49940  x  x  x
49940  x
Therefore, the silly number is 49940
5. Six less than triple a number is nine. Find that darn number!
3 x  6  99
3 x  99  6
3 x  105
3 x 105

3
3
x  35
Therefore, the darn number is 35.
6. Jane Fonda is three times as old as Adele. Together, their ages total one hundred. Find
the ages.
3 x  x  100
4 x  100
4 x 100

4
4
x  25
Therefore, Adele is 25 and Jane Fonda is 3 x 25 = 75 (she’s actually 76 in real life)
7. Twelve times a number decreased by twice the number is seventy. What’s the number?
12 x  2 x  70
10 x  70
10 x 70

10 10
x7
Therefore, the number is 7.
8. When a number is square rooted, the result is forty-nine.
x  49
2
x  49 2
x  2401
Therefore, the number is 2401
9. The length of a rectangle is twelve times the width. The perimeter is 130 cm. What are
the dimensions of the rectangle?
12 x  x  12 x  x  130
26 x  130
26 x 130

26
x
x5
Therefore, the width is 5cm and the length is 5 x 12 = 60cm
10. The sum of four consecutive numbers is one-hundred ninety-four. Find the numbers
x  x  1  x  2  x  3  194
4 x  6  194
4 x  194  6
4 x  188
4 x 188

4
4
x  47
Therefore, the numbers are 47, 48, 49, and 50
11. Each of the equal sides of an isosceles triangle is 12 cm greater than the base. The
perimeter is 96 cm. What is the length of each of the sides of the triangle?
x  x  12  x  12  96
3 x  24  96
3 x  96  24
3 x  72
3 x 72

3
3
x  24
Therefore, the side lengths are 24 cm, 36 cm, and 36 cm
12. A 14-year-old Lucas is about one-third as heavy as a black bear. Together, they weigh
one-hundred eighty kilograms. What is the mass of each creature?
x
 180
3
3x
3x 
 180(3)
3
3 x  x  540
x
4 x  540
4 x 540

4
4
x  135
Therefore, the bear is 135kg and Lucas is 180-135=45kg.
13. The width of a rectangle is four centimetres less that one-third the length. The
perimeter is 0.78m. What are the dimensions of the rectangle?
x
 4  x  39
3
x
 x  39  4
3
x
 x  43
3
3x
 3 x  43(3)
3
x  3 x  129
4 x  129
4 x 129

4
4
x  32.25
Therefore, the rectangle has a length of 32.25cm and a width of 32.25÷3-4 = 6.75cm
14. At the moguls competition at the Vancouver Olympics, the spectators were comprised
of three-fifths as many adults as youths (also pronounced yoots). Together, there were
20448 people in attendance that day. How many of each type of human were attending
the Olympic event that day?
3x
 x  20448
5
3x
(5)  5 x  20448(5)
5
3 x  5 x  102240
8 x  102240
8 x 102240

8
8
x  12780
Therefore, there are 12780 youths and 3(12780)÷5=7668 adults.
15. Maddie is twenty-two twenty-fifths as tall as Mr. Martindale. Together, their heights
are eleven feet nine inches. How tall is each human? This one is tough!
22 x
 x  11.75
25
22 x
(25)
 25 x  11.75(25)
25
22 x  25 x  293.75
47 x  293.75
47 x 293.75

47
47
x  6.25
Therefore, Mr. Martindale is 6 foot 3 inches tall and Maddie is 6.25(22)÷25=5.5 or 5
feet, 6 inches tall.
16. The perimeter of a triangle is 62 cm. The first side of the triangle is five centimetres
more than the second. The third side is three centimetres more than the second. How
long is each side?
x  x  5  x  3  62
3 x  8  62
3 x  62  8
3 x  54
3 x 54

3
3
x  18
Therefore, the 3 sides are 18cm, 21cm, and 23cm.
17. The perimeter of a regular octagon is 5cm. How long is each side?
8x  5
8x 5

8 8
x  0.375
Therefore, the sides are each 0.375cm long
18. Kareem is three times as old as Alonzo. Five years ago, the difference between their
ages was forty-eight years. How old is each turtle?
3 x  5  ( x  5)  48
3x  5  x  5
3 x  x  5  48  5
2 x 48

2
2
x  24
Therefore, Alonzo is 24 years old and Kareem is 24x3=72 years old.