Answer:
The cost of 1 notebook is $2.25
Step-by-step explanation:
First, we assign variables.
Let the cost of a notebook be $n while the cost of a pen be $p
Using Liz’s case, 3 pen boxes and 2 notebooks were bought.
Total cost of this is 3p + 2n = 16.5. •••••••(i)
Using Micheal’s case, 2 pen boxes and 1 notebook
Total cost = 2p + n = 10.25 •••••••(ii)
We now have two equations to solve simultaneously. From ii, n = 10.25 - 2p ; let’s insert this into i
3p + 2(10.25 -2p) = 16.5
3p + 20.5 - 4p = 16.5
4p - 3p = 20.5 - 16.5
p = $4
From the breakaway equation, n = 10.25 - 2p
n = 10.25 - 2(4)
n = 10.25 -8
n = $2.25
Answer: One notebook costs 2.25 dollars ($2.25)
Step-by-step explanation: To begin with we shall call each box of pen letter p and each notebook we shall call letter n. If Liz bought 3 boxes of pens and 2 notebooks for a total of 16.50 dollars, then this can be expressed as
3p + 2n = 16.5 ----------(1)
Similarly, Michael bought 2 boxes of the same pens and 1 of the same notebook for a total cost of 10.25. This we can express as
2p + n = 10.25 ----------(2)
We can now solve for the pair of simultaneous equations by applying the substitution method. In equation (2), make n the subject of the equation and we shall have
n = 10.25 - 2p
Substitute for the value of n into equation (1)
3p + 2(10.25 - 2p) = 16.5
3p + 20.5 - 4p = 16.5
Collect like terms and we now have
3p - 4p = 16.5 - 20.5
-p = -4
Multiply both sides of the equation by -1
p = 4
Having calculated the value of p, substitute for the value of p into equation (2)
2(4) + n = 10.25
8 + n = 10.25
Subtract 8 from both sides of the equation
n = 2.25
From our calculations one notebook (n) costs $2.25
