A friend bought 2 boxes of pencils and 8 notebooks for school and it cost him $11. He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would notebooks cost?
2 p + 8 n = 11 ... multiply by 3/2 ... 3 p + 12 n = 16.50
3 p + 5 n = 11.25
subtracting equations (to eliminate p) ... 7 n = 5.25
To find out how much the notebooks cost, we need to set up a system of equations based on the information given.
Let's assume the cost of each box of pencils is P dollars and the cost of each notebook is N dollars.
From the first purchase:
2P + 8N = 11 ------ Equation (1)
From the second purchase:
3P + 5N = 11.25 ------ Equation (2)
Now we can solve this system of equations to find the cost of the notebooks.
From Equation (1), we can rearrange it to isolate P:
2P = 11 - 8N
P = (11 - 8N)/2
Substituting this value of P into Equation (2):
3((11 - 8N)/2) + 5N = 11.25
Multiply both sides by 2 to eliminate the fraction:
3(11 - 8N) + 10N = 22.5
33 - 24N + 10N = 22.5
-14N = -10.5
Divide both sides by -14 to isolate N:
N = (-10.5)/(-14)
N = 0.75
So, each notebook costs $0.75.
To find out how much the notebooks cost, we can set up a system of equations based on the information given.
Let's use "p" to represent the cost of one box of pencils, and "n" to represent the cost of one notebook.
From the first purchase:
2p + 8n = 11 (equation 1)
From the second purchase:
3p + 5n = 11.25 (equation 2)
Now we can solve this system of equations to find the value of "n" (cost of one notebook).
Multiplying equation 1 by 3 and equation 2 by 2, we get:
6p + 24n = 33 (equation 3)
6p + 10n = 22.50 (equation 4)
Subtracting equation 4 from equation 3, we get:
14n = 10.50
Dividing both sides by 14, we find:
n = 0.75
Therefore, the cost of one notebook is $0.75.