5 books and 9 magazines cost $150.50 dollars altogether. 9 Books and 5 magazines cost $175.70. How much does 1 book and 1 magazine cost?
Please show work
Its something I need to have.
5b+9m=150.5
9b+5m=175.7 if you add them you have one equation.
14b+14m=326.2
14(b+m)=326.2
b+m=23.3
b=23.3-m
sub. this back into one the original equations
9(23.3-m)+5m=175.5
209.7-9m+5m=175.5
-4m=-34.2
m=8.55
Plug that into the other equation
5b+9(8.55)=150.5
5b+76.95=150.5
5b=73.55
b=14.71
Thanks!!!!!
To solve this problem, we need to set up a system of equations.
Let's assume the cost of 1 book is "b" dollars and the cost of 1 magazine is "m" dollars.
From the first equation, we can write:
5b + 9m = 150.50 ----(1)
From the second equation, we can write:
9b + 5m = 175.70 ----(2)
Now we can solve this system of equations to find the values of 'b' and 'm'.
First, let's multiply equation (1) by 9 and equation (2) by 5 to eliminate one variable. This will simplify the system:
45b + 81m = 1354.50 ----(3)
45b + 25m = 878.50 ----(4)
Subtracting equation (4) from equation (3) will eliminate 'b':
56m = 476
Dividing both sides by 56, we get:
m = 8.50
Now that we have found the value of 'm', we can substitute it into either equation (1) or (2) to find the value of 'b'. Let's use equation (1):
5b + 9(8.50) = 150.50
5b + 76.50 = 150.50
Subtracting 76.50 from both sides:
5b = 74
Dividing both sides by 5:
b = 14.80
Therefore, the cost of 1 book is $14.80 and the cost of 1 magazine is $8.50.