The total cost of 5 books, 6 pens and 3 calculators is $162. A pen and a calculator cost $29 and the total cost of a book and two pens is $22. Find the total cost of a book, a pen and a calculator?

where b = books, p = pen and c = calculators

Now put these values of c & b into eqn (i)

put the value of p in eqn(ii)

put the value of p in eqn (iii)

Let's denote the cost of a book as (b), the cost of a pen as (p), and the cost of a calculator as (c).

From the given information, we can form the following equations:

1. (5b + 6p + 3c = 162) (total cost of 5 books, 6 pens, and 3 calculators is $162)
2. (p + c = 29) (cost of a pen and a calculator is $29)
3. (b + 2p = 22) (total cost of a book and two pens is $22)

We can solve this system of equations to find the values of (b), (p), and (c).

First, we can use equation (3) to express (b) in terms of (p):

[ b = 22 - 2p ]

Now, substitute this expression for (b) into equations (1) and (2) to eliminate (b):

[ 5(22 - 2p) + 6p + 3c = 162 ] [ p + c = 29 ]

Simplify equation (1):

[ 110 - 10p + 6p + 3c = 162 ] [ 110 - 4p + 3c = 162 ] [ 3c = 162 - 110 + 4p ] [ 3c = 52 + 4p ] [ c = \frac{52 + 4p}{3} ]

Substitute the expression for (c) into equation (2):

[ p + \frac{52 + 4p}{3} = 29 ]

Now, solve for (p):

[ 3p + 52 + 4p = 87 ] [ 7p = 35 ] [ p = 5 ]

Now, substitute the value of (p) back into equation (3) to find (b):

[ b = 22 - 2(5) ] [ b = 22 - 10 ] [ b = 12 ]

Finally, substitute the values of (b) and (p) into equation (2) to find (c):

[ c = 29 - 5 ] [ c = 24 ]

Therefore, the total cost of a book, a pen, and a calculator is (b + p + c = 12 + 5 + 24 = 41).