Question

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.

Answer 1

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

$\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.$

We can solve this system using substitution

5x+3y=17

Divide by 5 to have a coefficient of 1 before x

$x+\frac{3}{5} y=\frac{17}{5}$

Subtract $\frac{3}{5} y$ from each side to single out one variable to one side

$x=\frac{17}{5} -\frac{3}{5} y$

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

$2(\frac{17}{5} -\frac{3}{5} y)+12y=23$

Open the parentheses

$\frac{34}{5} -1\frac{1}{5} y+12y=23$

Merge Y values

$6.8+10.8y=23$

Separate numerical values from variables

$10.8y=16.2$

Divide by 10.8 in order to have a coefficient of 1

$y=1.5$

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.

$5x+3(1.5)=17$

Open parentheses

$5x+4.5=17$

Single out the variable

$5x=12.5$

Divide by 5 to have a coefficient of 1 before x

$x=2.5$

$y=1.5$