Cost of 4 books and 5 pens is 32 and cost of 5 books and 4 pens is 31 then find the cost of 1 book B=?
answer choices?
4b + 5p = 32
5b + 4p = 31
Multiply first equation by 4 and second by 5.
16b + 20p = 128
25b + 20p = 155
Subtract first from second and solve for b.
To find the cost of one book, let's set up a system of equations using the given information.
Let's assume the cost of one book is B (in some currency units) and the cost of one pen is P (also in the same currency units).
From the first piece of information, we know that 4 books and 5 pens cost 32 units:
4B + 5P = 32 --------- Equation 1
From the second piece of information, we know that 5 books and 4 pens cost 31 units:
5B + 4P = 31 --------- Equation 2
We can solve this system of equations to find the values of B and P.
To eliminate P, let's multiply Equation 1 by 4 and Equation 2 by 5:
16B + 20P = 128 --------- Equation 3
25B + 20P = 155 --------- Equation 4
Now, subtract Equation 3 from Equation 4 to eliminate P:
(25B + 20P) - (16B + 20P) = 155 - 128
9B = 27
Dividing both sides of the equation by 9, we get:
B = 3
Therefore, the cost of one book is 3 units.