$ 45= 3 books 3 Pens
$ 177= 11 Books 12 Pens
Cost of b=
P=
3 p + 3b = 45
11 b + 12 p = 177
12 b + 12 p = 180
Subtract the second equation from the third.
b = 3.
9 + 12 p = 177
12 p = 168
p = ?
I made a mistake near the end.
3p + 9 = 45
3p = 36
p = 12
To find the cost of one book and one pen, we need to set up a system of equations using the given information.
Let's assume the cost of one book is represented by "b" and the cost of one pen is represented by "p".
From the first equation, we know that 3 books and 3 pens together cost $45. So, we can write the equation:
3b + 3p = 45
From the second equation, we know that 11 books and 12 pens together cost $177. So, we can write the equation:
11b + 12p = 177
Now, we have a system of two linear equations:
3b + 3p = 45
11b + 12p = 177
To solve this system of equations, we can either use substitution or elimination method. In this case, let's use the elimination method to eliminate one of the variables.
Multiply the first equation by 4 and the second equation by 1, so that the coefficients of "p" will cancel each other out when we add the equations:
12b + 12p = 180
11b + 12p = 177
Now, subtract the second equation from the first equation:
(12b + 12p) - (11b + 12p) = 180 - 177
This simplifies to:
12b - 11b = 3
b = 3
The cost of one book (b) is $3.
To find the cost of one pen, substitute the value of b into either of the original equations. Using the first equation:
3b + 3p = 45
Replace b with 3:
3(3) + 3p = 45
9 + 3p = 45
Subtract 9 from both sides:
3p = 36
Divide both sides by 3:
p = 12
The cost of one pen (p) is $12.
Therefore, the cost of one book is $3 and the cost of one pen is $12.