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Mathematics
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1. User Answers trent91houpt
To solve this I am going to create three equations for what each person bought.
a will represent apples, b will represent berries, and c will represent cherries.
34 = 2a + 1b + 4c
35 = 3a + 2b + 2c
49 = 5a + 3b + 2c
Solve for on variable in the first equation.
b = 34  2a  4c
Plug that into the second equation and solve for a different variable.
35 = 3a + 2(34  2a  4c) + 2c
35 = 3a + 68  4a  8c + 2c
35 = a + 68  6c
33 = a  6c
33 = a +6c
a = 33  6c
It gets a little confusing here but you plug in what both a and b are equal to until you have solved for c.
49 = 5a + 3b + 2c
49 = 5(33  6c) + 3b + 2c substitute a with 33  6c
49 = 165  30c + 3b +2c
49 = 165  28c + 3b
116 = 28c + 3(34  2a  4c) substitute b with 34  2a  4c
116 = 28c + 102  6a  12c
116 = 40c + 102  6(33  6c) again substitute a with 33  6c
116 = 40c + 102  198 + 36c
116 = 4c  96
20 = 4c
4c = 20
c = 5
a = 33  6c
a = 33  6(5)
a = 33  30
a = 3
b = 34  2a  4c
b = 34  2(3)  4(5)
b = 34  6  20
b = 8
Apples cost $3 per pound
Berries cost $8 per pound
Cherries cost $5 per pound