Math Help Please?

Question

A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?

Answer 1

Elimination by addition method

3o + 5l = 10.26- - - - - -Equation 1
60 + 4l = 11.16- - - - - -Equation 2
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Multiplty equation 1 by 4 and equaion 2 by - 5

3o + 5l = 10.26

4(3o) + 4(5l) = 4(10.26)

12o + 20l + 4104. . .New equation 1
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60 + 4l = 11.16

- 5(6o) +( - 5)(4l) = - 5(11.16)

- 30l + (- 20l) = - 55.8

- 30l - 20l -= - 55.8. . . New equation 2

Combine new equation 1 with new equation 2
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Elimination of l

12o + 20l = 41.04
- 30o - 20l = - 55.8
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- 18o = - 14.76

Divide both sides of the equation by - 18

- 18o / - 18 = - 14.76 / - 18

o = - 14.76 / - 18

0 = 0.82. . .Price of oranges

Insert the o value into equation 1
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3o + 5l = 10.26

3(0.82) + 5l = 10.26

2.46 + 5l = 10.26

Transpose 2.46

2.46 + 5l - 2.46 = 10.26 - 2.46

5l = 7.8

Divide both sides of the equation by 5

5l / 5 = 7.8 / 5

l = 7.8/5

l = 1.56, , ,Price of lemons

Insert the l value into equation 1
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Check for equation 1

3o + 5l = 10.26

3().82) + 5(1.56) = 10.26

2.46 + 7.8 = 10.26

10.86 = 10.26

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Check for equation 2

6o = 4l = 11.16

6(0.82) + 4(1.56) = 11.16

4.92 + 6.24 = 11.16

11.16 = 11.16

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Both equation balance

The solution set is { 0.82, 1.56 }

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Answer 2

just make it into 2 algebra equations w/ the same variables.
i.e. 3o + 5 l = 10.26 is the first equation.
then use o and l in the next equation. then use something like gaussian elimination (basically add or subtract one multiple of one equation from the other so as to eliminate a variable, like o + l = 7.5 and 2o +3l = 20 then means that if you subtract twice the eq. from the second, you'd get 2o + 3l - (2o + 2l) = 20-(2*7.5). which is the same as l = 5. which you could then plug into either equation to solve. like 2o + 3*5 = 20, or 2o = 5, or o = 2.5.

Answer 3

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Answer 4

use a clculater

this is sorta like cheating

Answer 5

is it in your test paper???or just asking from your friends?