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A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $17. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $23. Find the cost for each pound of trail mix and each pound of jelly beans.

Sagot :

Answer:

Trail Mix costs $2.50 per pound, and Jelly Beans cost $1.50 per pound.

Step-by-step explanation:

Using x for trail mix and y for jelly beans, we have a system of equations being

[tex]\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.[/tex]

We can solve this system using substitution

5x+3y=17

Divide by 5 to have a coefficient of 1 before x

[tex]x+\frac{3}{5} y=\frac{17}{5}[/tex]

Subtract [tex]\frac{3}{5} y[/tex] from each side to single out one variable to one side

[tex]x=\frac{17}{5} -\frac{3}{5} y[/tex]

Now, we can plug in our value for x into the given equation

[tex]2(\frac{17}{5} -\frac{3}{5} y)+12y=23[/tex]

Open the parentheses

[tex]\frac{34}{5} -1\frac{1}{5} y+12y=23[/tex]

Merge Y values

[tex]6.8+10.8y=23[/tex]

Separate numerical values from variables

[tex]10.8y=16.2[/tex]

Divide by 10.8 in order to have a coefficient of 1

[tex]y=1.5[/tex]

Now that we have one of the values, we know that a pound of jelly beans costs $1.50. We can now plug in 1.5 for y into one of our equations to find x.

[tex]5x+3(1.5)=17[/tex]

Open parentheses

[tex]5x+4.5=17[/tex]

Single out the variable

[tex]5x=12.5[/tex]

Divide by 5 to have a coefficient of 1 before x

[tex]x=2.5[/tex]

[tex]y=1.5[/tex]

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