Jim paid $ 5.55 for 1 notepad and 7 pencils. Anne paid $ 12.28 for 3 notepads and 2 pencils. How much does each notepad cost? Show all work
1n + 7p = 5.55
3n + 2p = 12.28
from the first:
n = 5.55-7p
sub into the 2nd
3(5.55-7p) + 2p = 12.28
16.65 - 21p + 2p = 12.28
-19p = -4.37
p = .23
then n = 5.55 - 7(.23) = 3.94
check:
1 notebook + 7 pencils
= 3.94 + 7(.23) = 5.55
3 notebooks + 2 pencils
= 3(3.94) + 2(.23) = 12.28
checks out!
1n+7p = 5.55
3n+2p = 12.28
that's the same as
2n+14p = 11.10
21n+14p = 85.96
now subtract to get rid of the p's
19n = 74.86
n = 3.94
To solve this problem, we can set up a system of equations.
Let's represent the cost of one notepad as "x" and the cost of one pencil as "y."
From the first sentence, we can write the equation:
1x + 7y = 5.55
From the second sentence, we can write the equation:
3x + 2y = 12.28
Now, we can use the method of substitution to solve the system.
First, we solve one equation for one variable:
From the first equation, we can solve for x:
x = 5.55 - 7y
Next, we substitute this expression for x in the second equation:
3(5.55 - 7y) + 2y = 12.28
Now, we simplify and solve for y:
16.65 - 21y + 2y = 12.28
16.65 - 19y = 12.28
16.65 - 12.28 = 19y
4.37 = 19y
y = 4.37 / 19
y = 0.23 (rounded to the nearest two decimal places)
Now that we have the value for y, we can substitute it back into either of the original equations to find the value for x:
From the first equation:
1x + 7(0.23) = 5.55
1x + 1.61 = 5.55
1x = 5.55 - 1.61
1x = 3.94
x = 3.94
Therefore, the cost of each notepad is approximately $3.94.
To find out how much each notepad costs, we need to set up a system of equations using the given information.
Let's say the cost of one notepad is "x" dollars and the cost of one pencil is "y" dollars.
From the given information, we can set up the following equations:
1) Jim paid $5.55 for 1 notepad and 7 pencils:
x + 7y = 5.55
2) Anne paid $12.28 for 3 notepads and 2 pencils:
3x + 2y = 12.28
Now, we need to solve this system of equations to determine the values of "x" and "y".
There are several methods to solve this system, such as substitution or elimination. In this case, we will use the elimination method:
To eliminate "y", we will multiply Equation 1 by 2 and Equation 2 by 7:
2(x + 7y) = 2(5.55) --> 2x + 14y = 11.1
7(3x + 2y) = 7(12.28) --> 21x + 14y = 85.96
By subtracting Equation 1 from Equation 2, we can eliminate "y":
(21x + 14y) - (2x + 14y) = 85.96 - 11.1
Simplifying the equation, we get:
19x = 74.86
Dividing both sides of the equation by 19, we find:
x = 74.86 / 19
Calculating this, we get:
x ≈ 3.94
Therefore, each notepad costs approximately $3.94.