Can any one help me with my algebra homework?

Question

Three pens and two notebooks cost $8.25. Two pens and three notebooks cost $8.00. How much would a pen and a notebook cost?

Answer 1

let p = pens and n = notebooks
3p + 2n = 8.25
2p + 3n = 8.00
add these two equations together
5p + 5n = 16.25
p + n = 3.25

hope this is what you were looking for :-)

Answer 2

If three pens and two notebooks cost $8.25, then six pens and four notebooks would cost twice as much, $16.50, unless there was a discount for quantity.

If two pens and three notebooks cost $8.00, then six pens and nine notebooks would cost three times as much, $24.00, again exceptng the case of discounts.

Comparing these two calculations, we see that the second has five more notebooks than the first, and costs $7.50 more. So, unless the retailer has some fancy calculation going, five notebooks cost $7.50, implying that each is $1.50.

Well, if one notebook is $1.50, then two is $3.00. But two notebooks and three pens costs $8.25. So the three pens must have cost 8.25 less 3.00 which is $5.25. Again, unless the retailer is being shifty.

And if three pens cost $5.25, then each costs a third of that, which is $1.75.

So, one notebook costs $1.50, and one pen costs $1.75. So, they cost 1.50 + 1.75 = $3.25 together, assuming the retailer hasn't done something even more awful!

Answer 3

Use the letter p for pens and n for notebooks. The first equation is 3p+2n=8.25 and the second equation is 2p+3n=8.00. Use these two equations to find the values of p (the price of one pen) and, using the value for p, plug it back into one of the equations and solve for n (the price for one notebook). Add p and n together to find the total price for one of each.

Answer 4

Everyone is learning systems of equations tonite. :)
ok so lets use the letter P to mean pens and the letter N to mean notebooks:

3 pens and two notebooks = 3P + 2N
since their total cost is 8.25 we can write:
3P + 2N = 8.25

Two pens and 3 notebooks = 2P + 3N
their total cost is 8.00 so:
2P + 3N = 8.00

So now you have two equations for two unknown variables (P and N)

Lets solve for the P:
2P + 3N = 8.00
2P = 8.00 - 3N
P = 4.00 - (3/2)N

Ok so now we know what P is...but it has a letter still in the answer so lets "plug it in" the other equation we know to get rid of the letter and get a number:

3P + 2N = 8.25
3(4.00 - (3/2)N) + 2N = 8.25
12.00 - (9/2)N + 2N = 8.25
12.00 - 13/2N = 8.25
(-13/2)N = 8.25 - 12.00
(-13/2)N = -3.75
N = -3.75(-2/13)

Answer 5

Let p be the cost of a pen and n be the cost of a notebook. Then you know that

3p + 2n = 8.25

2p + 3n = 8

And you can solve the system from there. If you don't like decimal points, you could write them as

3p + 2n = 825
2p + 3n = 800

Your answers for p and n would then be in pennies.

Answer 6

mdigitale did a beautiful job laying out how to solve for "P" and "N" but the adding error makes the final list of equations incorrect.
last correct line: 12-9/2N+2N=8.25
-9/2N+2N=8.25-12
-9/2N+4/2N=-3.75
-5/2N=-3.75
N=-3.75/-2.5
N=1.50

Answer 7

I get $3.25, $1.50 for the notebook and $1.75 for the pen

Answer 8

check the price tag