Algebra 1 Word Problems

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Various day-to-day mathematical problems or the real world problems can be easily solved by first converting the problem in the form of an equation and then solving it by applying the rules of algebra. Algebra 1 word problems tool helps in solving the word problem step by step.

This can be illustrated by a few examples as below.

Example 1: If the cost of 12 pens is $50, find the cost of 5 such pens.

Solution:

Here we cannot find the cost of 5 pens unless we find the cost of one pen, which is also not known, from the question.

We start by assuming the cost of one pen to be ‘x’,

So the cost of 12 pens would be 12 (x) = 12x……………….. (1)

But according to the question cost of 12 pens = $50….…. (2)

So from the equation (1) and (2) above, we get

12x = 50

Dividing both sides by 12

12x/12 = 50

x = 4.16, i.e. the cost of one pen………… (3)

Now, cost of 5 pens would be 5x. But x = 4.16 as per equation (3)

So, cost of 5 pens = 5 X 4.16 = $20.8
 
Example 2: Find the cost of a bag which was sold for $200 at a profit of 20%.

Solution:

Let us assume the cost price (C.P) to be =x

We know that,

Selling price (S.P) = C.P + Profit

Or S.P = C.P + P

Or, S.P = x + 20% of x (because profit is 20% of the C.P)

Or, S.P = x + 20x/100

Or, S.P. =120x/100…………………………………..(1)

But according to the question S.P = 200……….(2)

From equation (1) and (2) above

= 200

Multiplying both sides by 100

Or, 120x/100 * 100 = 200 x 100

Or,120x = 20000

Dividing both sides by 120

120x/120 = 20000/120

X= 166.67, or the cost price of the bag was $166.66

 

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