Algebra Word Problems

Examples on Algebra Word Problems

1) The three angles in a triangle are in the ratio of 2:3:4. Find the measure of each angle.

Solution :
Let the ratio = x

As in the triangle, sum of all the three angles = 180
0

2x + 3x + 4x = 180

9x = 180

X = 20

Each angle,

2x = 2( 20) = 40
0

3x = 3(20) = 60
0

4x = 4(20) = 80
0
_________________________________________________________________
2) The sum of 3 consecutive even numbers is 78. Find the numbers.

Solution :
Let the 3 consecutive even numbers are x, x+2 and x+4.

Therefore,

x + (x + 2) + (x + 4) = 78

Or 3x + 6 = 78

Or 3x = 78 – 6 = 72

Or x = 24 (Divide both sides by 3)

So the three numbers are 24,26,18.
_________________________________________________________________
3) There are 650 students in a school. If the number of girls is 106 more than the boys, how many boys are there in the school?

Solution :
Let the number of boys = x

Then, number of girls = x + 106

x + (x + 106) = 650 (Given in the question)

Or 2x + 106 = 650

Or 2x = 650 – 106 = 544

Or x = 272

Hence, the number of boys = 272

And, the number of girls = (x + 106)

= 272 + 106

= 378
_________________________________________________________________
4) I have a total of $300 in coins of denomination $1, $2 and $5. The number of $2 coins is 3 times the number of $5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Solution
Let $5 coin = x
∴ $2 coins = 3x
Total number of coins = 160
So, $1 coin = 160 - (x +3x)= 160 -4x
Total money = $300
∴ 5(x) + 2(3x) + 1(160 -4x)=300
⇒ 5x + 6x + 160 - 4x = 300
⇒ 11x -4x + 160 =300
⇒ 7x + 160 =300
⇒ 7x = 300 -160
⇒ 7x = 140
So, $5 coins are 20
$2 coins = 3x = 3(20)=60
$1 coins = 160 -(20 + 60)
$1 coins = 80
________________________________________________________________________

Linear Equation in One Variable

Linear Equation in One Variable
Algebraic Equations with Fractions
Algebra Word Problems
Algebra Rate (upstream and downstream) Problems
Algebra Age Problems
Algebra Digit Problems

Home Page