Three notebooks, 2 binders and 1 pack of pencils costs $6. Twonotebooks, 1 binder and 2 packs of pencils costs $6.92. One notebook, 3 binders and 3 packs of pencils costs $10.84. How much does one binder cost?
+1094 I wonder why that person has the time to see how much the totals cost, when he/she could have just checked the price...
Whatever the case, we need to help the person out, because they could not bother to go and check the unit price, and decided to create a math problem for it.
To start, let's label each item with a variable.
Notebook = n
Binder = b
Pencil = p
With these variables set, we can create some equations!
3n + 2b + p = 6
2n + b + 2p = 6.92
n + 3b + 3p = 10.84
We see that here are 3 variables, which means this is a 3 variable system of equations .
Add the two top equations:
5n + 3b + 3p = 12.92
Subtract bottom equation:
4n = 2.08
n = 0.52
Now that we know how much a notebook costs, we can plug that value back into the equations:
3(0.52) = 1.56
2(0.52) = 1.04
1(0.52) = 0.52
So:
1.56 + 2b + p = 6
2b + p = 4.44
1.04 + b + 2p = 6.92
b + 2p = 5.88
0.52 + 3b + 3p = 10.84
3b + 3p = 10.32
We now know that:
p = 4.44 - 2b
So:
b + 2(4.44 - 2b) = 5.88
b + 8.88 - 4b = 5.88
-3b = -3
b = 1
Therefore, à binder costs one dollar.
Also, it would be nice if you actually read my answer from start to end, because it took me 27 minutes to compose it.
:)
+15001 Three notebooks, 2 binders and 1 pack of pencils costs $6. Twonotebooks, 1 binder and 2 packs of pencils costs $6.92. One notebook, 3 binders and 3 packs of pencils costs $10.84. How much does one binder cost?
Hello Guest!
3n+2b+p=6
2n+b+2p=6.92
n+3b+3p=10.84
\(3n+2b+p=6\\ 2n+b+2p=6.92\\ n+3b+3p=10.84 \)
\(n=(6-2b-p)/3\\ n=(6.92-b-2p)/2\\ n=10.84-3b-3p\)
\((6-2b-p)/3=(6.92-b-2p)/2\\ 10.84-3b-3p=(6.92-b-2p)/2\)
\(2-\frac{2}{3}b-\frac{1}{3}p=3.46-\frac{1}{2}b-p\\ \frac{2}{3}p=3.46-2+\frac{1}{6}b\\ p=\frac{4.38+\frac{1}{2}b}{2}\\ \color{blue}p=2.19+\frac{1}{4}b \)
\(10.84-3b-3p=(6.92-b-2p)/2\\ 10.84-3b-3p=3.46-\frac{1}{2}b-p\\ 7.38-\frac{5}{2}b=2p \)
\(p=3.69-\frac{5}{4}b\)
\(3.69-\frac{5}{4}b=2.19+\frac{1}{4}b\\ 3.69-2.19=\frac{6}{4}b\)
\(b=1\)
A binder costs 1 $.
n = 0,5200000000000005 at Brünner
b = 0,9999999999999997
p = 2,44
!
