Problem Page A store is having a sale on jelly beans and trail mix. For 8 pounds of jelly beans and 4 pounds of trail mix, the total cost is $25 . For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $10 . Find the cost for each pound of jelly beans and each pound of trail mix.

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absor201 absor201 · Answer 1 · 2019-12-08T18:38:35+01:00

Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25

Step-by-step explanation:

Let,

Cost of jelly beans = x

Cost of trail mix = y

According to given statement;

8x+4y=25 Eqn 1

3x+2y=10 Eqn 2

Multiplying Eqn 2 by 2;

[tex]2(3x+2y=10)\\6x+4y=20\ \ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1;

[tex](8x+4y)-(6x+4y)=25-20\\8x+4y-6x-4y=5\\2x=5[/tex]

Dividing both sides by 2;

[tex]\frac{2x}{2}=\frac{5}{2}\\x=2.5[/tex]

Putting x=2.5 in Eqn 1

[tex]8(2.5)+4y=25\\20+4y=25\\4y=25-20\\4y=5[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{5}{4}\\y=1.25[/tex]

Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25

Keywords: linear equations, subtraction

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