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A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $31. For 5 pounds of trail mix and pounds of 2 jelly beans, the total cost is 12. Find the cost for each pound of trail mix and each pound of jelly beans.

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Answer:

trail mix costs 1.00 per pound

jelly beans costs 3.50 per pound

Step-by-step explanation:

t = cost of trail mix

b = cost of jelly beans

3t+8b = 31

5t+2b = 12

Multiply the second equation by -4

-4(5t+2b = 12)

-20t+-8b = -48

Add this to the first equation

3t+8b = 31

-20t+-8b = -48

-------------------------

-17t = -17

Divide by -17

t = 1

Now we can find b

3t+8b = 21

3(1) +8b = 31

3+8b =31

Subtract 3

8b = 31-3

8b = 28

Divide by 8

b = 28/8

b = 7/3

b = 3.50

Let trail mix be x and jelly beans be y

The equations are

  • 3x+8y=31-(1)
  • 5x+2y=12-(2)

Multiplying (1) by 1 and (2) by 4

  • 3x+8y=31---(3)
  • 20x+8y=48--(4)

Subtracting

[tex]\\ \sf\longmapsto -17x=-17[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Putting in eq(2)

[tex]\\ \sf\longmapsto 5(1)+2y=12[/tex]

[tex]\\ \sf\longmapsto 2y=7[/tex]

[tex]\\ \sf\longmapsto y=7/2[/tex]

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