Algebra is a branch of mathematics which involves the study of variables,constants and finding out the unknown variables In this section we shall help in solving the statement problems in algebra which emphasis on enhancing the skills of building an algebraic equation and solving them.

## Algebra 2 Homework Help

**Example 1**Peter is 20 years older than Dave and the next year he will be twice has old as peter.How old they are now ?

**Step1** First we shall try to write the above statement in a mathematical way that is build an equation to this statement

**Step2** We shall use "p" as the variable for peter and "d" as the variable for dave.

**Step3** Construct an algebraic equation.

**Step4** p = 20+d --- This is according to the first statement ( Peter is 20 yrs older than Dave)--------- (1)

**Step5** p+1= 2(d+1) This is according to the second statement ( He (peter ) will be twice as old as peter )

**Step6** p+1= 2d+2 ----- p-2d =1-------- (2)

**Step7 Solving equation (1) and(2)**

step8 p-d=20

(-) p-2d=1

(+)

_________________

d= 21

_________________

we got dave's age has 21 years

Peter's age will be p-21=20 ( substuting in equation 1)

We get p=20+21

p= 41 yrs.

**Solution : Peters age is 41 years and daves age is 21 years**.

**Example 2**The First stage of a space ship burns the rocket 52 seconds more than the second stage. If the total burn time for both stages is 180 seconds find the time taken to burn in each stage of the space ship rocket.

**Step1**: Here Let each burn stage be denoted by x

**Step2**:According to the the statement the first stage of a space ship burns the by 52 seconds more the second stage so mathematically this becomes x+x+52=160 Here x is the 1st stage x+52 is the second stage

**Step3** 2x+52=160

2x=160-52

2x=108.

x= 108/2

x=54 seconds.

Solution : The time taken to burn in each stage is 54 seconds.**Example 3** The sum of two numbers is 100 and one of them is 20 more than the other. find the numbers.

**Step 1** Let the first number be x

**Step 2** So according to the statement second number is is 20 more than the first one

**Step3 **The equation becomes x+x+20=100

**Step4** 2x+20=100

**Step5** 2x=100-20

**Step6** 2x=80 x=80/2=40

**Solution : The first number is 40 and the second number is x+20 that is 40+20 = 60 ****Example 4**The sum of two consecutive numbers is 41 find the numbers.

Step1 Let two consecutive integers be x and x+1

Step2 Their sum is x+x+1 =41

**step3** 2x+1=41

**step4 **2x=41-1

**Step5** 2x=40

**Step6** x=40/2

**Step7** x=20

**Solution : The two consective integers are x=20 and x+1 that is 20+1= 21. ( Verification 20+21=41 ,so our solution is correct)**