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Applications To Word Problems
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Applications To Word Problems
Word Problems are related with our day to day life. Here we are using simultaneous linear equations in solving word problems.
Follow the following Algorithm
STEP I Read the problem carefully and identify the unknown quantities. Give these quantities a variable name like x, y, u, v, w etc.
STEP II Identify the variables to be determined.
STEP III Read the problem carefully and formulate the equations in terms of the variables to be determined.
STEP IV Solve the equations obtained in step III by using any one of the methods learnt earlier.
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Example: 37 pens and 53 pencils together cost $ 320, while 53 pens and 37 pencils together cost $ 400. Find the cost of a pen and that of a pencil.
Solution: Let the cost of a pen be $ x and that of a pencil be $ y. Then,
37x + 53y = 320 ...(i)
and, 53x + 37y = 400 ...(ii)
Adding equations (i) and (ii), we get
90x + 90y = 720 => x + y = 8 ...(iii)
Subtracting equations (i) from (ii), we get
16x -16y = 80 => x - y = 5 ...(iv)
Adding equations (iii) and (iv), we get
2x = 13 => x = 6.5
Substituting x = 6.5 in equation (iii), we get
y = (8 - 6.5) = 1.5.
Hence, cost of one pen = $ 6.50. and, cost of one pencil = $ 1.50.
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