SOLUTION: Newman's Fine Haberdashery store is having its annual spring sale You can buy suspenders and socks for $18. You can buy socks and a tie for $22. You can buy a tie and cufflinks for

Question 654894: Newman's Fine Haberdashery store is having its annual spring sale You can buy suspenders and socks for $18. You can buy socks and a tie for $22. You can buy a tie and cufflinks for $25. You can buy a shirt and a belt for $37. You can buy cufflinks and a shirt for $33. You can buy a belt and socks for $17. How much does each article cost?
I need to learn how to do this, set up the equation and solve it. Not just the answer.
thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Newman's Fine Haberdashery store is having its annual spring sale
You can buy suspenders and socks for $18.
You can buy socks and a tie for $22.
You can buy a tie and cufflinks for $25.
You can buy a shirt and a belt for $37.
You can buy cufflinks and a shirt for $33.
You can buy a belt and socks for $17.
How much does each article cost?
:
Assign variables to each item
a = suspenders
b = socks
c = ties
d = cufflinks
e = shirts
f = belts
:
Write an equation for each statement
Try to get as many variables as possible in terms of b
:
You can buy suspenders and socks for $18.
a + b = 18
a = (18-b)
:
You can buy socks and a tie for $22.
b + c = 22
c = (22-b)
:
You can buy a tie and cufflinks for $25.
c + d = 25
replace c with (22-b)
(22-b) + d = 25
d = 25 -(22-b)
d = 25 - 22 + b
d = b + 3
:
You can buy a shirt and a belt for $37.
e + f = 37
:
You can buy cufflinks and a shirt for $33.
d + e = 33
e = (33-d
Replace d with (b+3)
e = 33 - (b+3)
e = 33 -3 - b
e = (30-b)
:
You can buy a belt and socks for $17.
f + b = 17
f = (17-b)
:
We have e + f = 37, replace e with (30-b), replace f with (17-b)
(30-b) + (17-b) = 37
47 - 2b = 37
47 - 37 = 2b
10 = 2b
b = $5 for socks
:
Find a
a = 18 - b
a = 18 - 5
a = $13 for suspenders
:
Find c
c = 22-5
c = $17 for ties
:
Find d
d = 5 + 3
d = $8 for cuff links
:
Find e
e = 30 - 5
e = $25 for a shirt
:
Find f
e + f = 37
25 + f = 37
f = 37-25
f = $12 for a belt
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