# Questions - Algebra & Equations

Other words that mean equal
is the same as
balances
has the same value as
makes

1) What is Algebra ?
A part of maths that deals with finding missing numbers in equations.

2) I think of a number. I divide it by three and add four. I get an answer of 9. What number was I thinking of ?
(N / 3) + 4 = 9
(N / 3) = 9 - 4
(N / 3) = 5
N = (5 * 3) = 15

3) Can you simplify (a + a + a) ?
Another word for simplifying is collecting "Like" terms.

4) What number, when divided by 12, has an answer of 11 remainder 5 ?
(12 x 11) = 132
132 + 5 = 137

5) A number when divided by 3000 leaves the remainder 70. If the same number is divided by 24, what is the remainder ?
N = 3000q + 70
N = (125*24)q + 48 + 22
N = 24 (125q + 2) + 22
N = 24p + 22 ( Here p=125q+2 is an integer)
Thus when N is divided by 24 ,the remainder =22

6) Can you solve this ?
f + 2g = 4h
f + 2g - 4h = 0
0 = f + 2g - 4h (which is exactly the same as this)
Left Side = Right Side
Right Side = Left Side

7) 7A + 1 = 9B + 3
Is it possible to solve for two variables related by a single equation - ?? YES

8) How many beads does Lina have ?
If they are arranged into piles of 7, there is one bead left over.
If they are arranged into piles of 9, there are three beads left over.
List all the numbers that give remainder 1 when you divide by 7
8, 15, 22, 29, 36, 43, 50, 57
List all the numbers that give remainder 3 when you divide by 9
12, 21, 30, 39, 48, 57
57 = 7A + 1
56 = 7A
A = 8
57 = 9B + 3
54 = 9B
B = 6
Total number of beads is 57.

9) What is the equation of a straight line in its standard form ?
y = mx + c

10) Barry will be N years old in four years time.
How old was he eight years ago in terms of N ?
B = N - 4
B = (N - 4) - 8
B = N - 12