SOLUTION: Hi there! Stupid stuck! (Again!) Joe buys five shirts and three shorts for $51. Bill buys three shirts and seven shorts for $80. How much does each shirt and each pair of sh

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Question 652169: Hi there! Stupid stuck! (Again!)
Joe buys five shirts and three shorts for $51.
Bill buys three shirts and seven shorts for $80.
How much does each shirt and each pair of shorts cost.
So, if x is cost of each shirt
And if y is the cost of each pair of shorts, wouldn't the restated problem be:
8x + 10y = $131? Where do I go from here. I am stuck, again.

Found 2 solutions by nerdybill, MathLover1:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Joe buys five shirts and three shorts for $51.
Bill buys three shirts and seven shorts for $80.
How much does each shirt and each pair of shorts cost.
So, if x is cost of each shirt
And if y is the cost of each pair of shorts
.
gives you the "system of equations":
5x + 3y = 51
3x + 7y = 80
solve by the "addition method".
multiply top eq by 3 and bottom eq by -5 then combine both:
15x + 9y = 153
-15x -35y =-400
----------------
-26y = -247
y = $9.50 (shorts)
.
shirts:
5x + 3y = 51
5x + 3(9.50) = 51
5x + 28.50 = 51
5x = 22.50
x = $4.50

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
Joe buys 5 shirts and 3 shorts for $51.
Bill buys 3 shirts and 7 shorts for $80.
if+x is cost of each shirt and if y is the cost of each pair of shorts, than we have:
+5x%2B3y=51....1....what Joe buys
+3x%2B7y=80....2....what Bill buys
____________________________________.....solve the system
+5x%2B3y=51....1...solve for x
+5x=51-3y
+x=51%2F5-3y%2F5..........plug it in 2 and solve for y
+3%2851%2F5-3y%2F5%29%2B7y=80....2
+153%2F5-9y%2F5%2B7y=80....each term multiply by 5
+153%2A5%2F5-9%2A5y%2F5%2B7%2A5y=80%2A5
+153%2Across%285%29%2Fcross%285%29-9%2Across%285%29y%2Fcross%285%29%2B35y=400
+153-9y%2B35y=400
+26y=400-153
+26y=247
+y=247%2F26
+highlight%28y=9.5%29..........cost of each each pair of shorts
now find x
+x=51%2F5-3y%2F5
+x=10.2-3%289.5%29%2F5
+x=10.2-28.5%2F5
+x=10.2-5.7
+highlight%28x=4.5%29......cost of each shirt