## Solving Algebra Word Problems

### Solved Examples

**Question 1:**Five times Madona's age plus four years is Stefen's age. Stefen is 24 years old. Find Madona's age.

**Solution:**

Step 1:

Let Madona's age = x

Stefen's age = 24

The statement states:

5 times Madona's age + 4 = Stefen's age

=> 5x + 4 = 24

Solve for x,

Subtract 4 from both sides of the equation

=> 5x + 4 - 4 = 24 - 4

=> 5x = 20

Divide each side by 5

=> $\frac{5x}{5} = \frac{20}{5}$

=> x = 4

**Question 2:**

Find the numbers such that twice of the first number added to four times of the second number gives 800 and five times of first number added to the two times the second number gives 720.

**Solution:**

**Step 1:**

Twice of the first number + four times of the second number = 800

=> 2x + 4y = 800 ..........................(1)

Five times of first number + two times the second number = 720

=> 5x + 2y = 720 .............................(2)

**Step 2:**

Multiply equation (1) by 5 and equation (2) by 2

=> 5(2x + 4y) = 800 * 5

=> 10x + 20y = 4,000 ..............................(3)

and

2(5x + 2y) = 720 * 2

=> 10x + 4y = 1440 .............................(4)

**Step 3:**Subtract equation (4) from equation (3)

=> 10x + 20y - (10x + 4y) = 4000 - 1440

=> 10x + 20y - 10x - 4y = 2560

=> 16y = 2560

Divide both sides by 16

=> $\frac{16y}{16} = \frac{2560}{16}$

=> y = 160

**Step 4:**

Put y = 160 in equation (1)

=> 2x + 4 * 160 = 800

=> 2x + 640 = 800

=> 2x = 800 - 640 = 160

=> x = $\frac{160}{2}$ = 80

=> x = 80

Hence the numbers are 80 and 160.