Practice Solving Algebra Equations – with Video Solutions

5. D
The price increased from $20 to $25 ($5) so the question is 5 is what percent of 20. Or, 5/20 = x/100 ; 500/20 = 25%

6. C

7. D
The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so,
150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100
so 150 + 45 = 195

8. B

Let us call this number by x:

This number is increased by 2: x + 2

Then, it is multiplied by 3: 3(x + 2)

The result is 24: 3(x + 2) = 24 … Solving this linear equation, we obtain the value of the number:

3(x + 2)/3 = 24 /3   Divide both sides by 3 and cancel  out

x + 2 = 24 / 3

x + 2 = 8

x = 8 – 2   – 2 crosses the equal sign so negative

x = 6

9. B

My age: x

My brother is 3 years older than me: x + 3

My father is 3 less than 2 times my age: 2x – 3

My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3

By cross multiplication:

5(x + 3) = 3(2x – 3)

5x + 15 = 6x – 9

x = 24

My father’s age: 2^.24 – 3= 48 – 3 = 45

10. C

There are two fractions containing x and the denominators are different. First, let us find a common denominator to simplify the expression. The least common multiplier of 4 and 7 is 28. Then,

7(x – 2) / 28 – 4(3x + 5) / 28 = – 3^.28 / 28 … Since both sides are written on the denominator 28 now, we can eliminate them:

7(x – 2) – 4(3x + 5) = – 84

7x – 14 – 12x – 20 = – 84

– 5x = – 84 + 14 + 20

– 5x = – 50

x = 50/5

x = 10

11. B

We can follow outside to inside method to solve this type of problems. x is in the inner part of this fraction; then, we need to narrow the circle to reach x:

1 / (1 + 1 / (1 – 1/x)) = 4

This means that (1 + 1 / (1 – 1/x)) is equal to 1/4. Then,

1 + 1 / (1 – 1/x) = 1/4

1 / (1 – 1/x) = 1/4 – 1

1 / (1 – 1/x) = – 3/4

This means that 1 – 1/x = – 4/3. Then,

1 – 1/x = – 4/3

1 + 4/3 = 1/x

1/x = 7/3

So, x = 3/7.