SOLUTION: A man bought at one time 3 bushels of wheat and 5 bushels of rye for 38 shillings; and at another time 6 bushels of wheat and 3 bushels of rye for 48 shillings. What was the price

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Question 1301: A man bought at one time 3 bushels of wheat and 5 bushels of rye for 38 shillings; and at another time 6 bushels of wheat and 3 bushels of rye for 48 shillings. What was the price of each bushel?
Found 2 solutions by iamlegallyblond7, DeepaEvangeline:
Answer by iamlegallyblond7(7) (Show Source):
You can put this solution on YOUR website!
W= BUSHELS OF WHEAT
R= BUSHELS OF RYE
3W+5R=38
6W+3R=48
SOLVE ONE EQUATION FOR ONE VARIABLE:
EXAMPLE: 3R=48-6W
R=16-2W
PLUG THIS INTO THE OTHER EQUATION
3W+5(16-2W)=38
3W+80-10W=38
-8W=-42
W=42/8
PLUG THIS INTO THE OTHER EQUATION IN ORDER TO FIND THE VALUE OF R

Answer by DeepaEvangeline(15) (Show Source):
You can put this solution on YOUR website!
Let x be the price of wheat bushel
Let y be the price of rye bushel
Therefore 3x + 5y = 38 -----(1)
6x + 3y = 48 ------(2)
Solving eqn (1) & (2)
Eliminate x by multiplying eqn (1) by 2
Eqn (1) becomes, 6x + 10y = 76 -----(3)
Eqn (3) - (1) gives
7y = 28
y = 28/7 = 4
Substitute y = 4 in eqn (1)
3x + 5*4 = 38
3x + 20 = 38
3x = 18
x = 18/3 = 6
Price of wheat bushel is 6
Price of rye bushel is 4