Question

A store is having a sale on jelly beans and trail mix. For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $30 . For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $12. Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

For this question, you'll solve it using simultaneous equations.

You can name jelly bean, j and trail mix, t. These will be the variables for the equations.

Answer 2

It says 5 pounds of jelly beans and 6 pounds of trail mix has a total cost of $30.
It also 3 pounds of jelly beans and 2 pounds of trail mix has a total cost of $12.

The first statement will have the equation : 5j + 6t = 30. And the second statement will be 3j + 2t = 12

Answer 3

the equations will

5j+6t = 30 ---- equ. 1
3j+2t=12 ---equ. 2

We need to find the values for each variable, j and t. First we need to see which is easier to eliminate. We can eliminate the variable t by multiplying equation 2 by -3 and equation 1 by 1.

We'll get
5j+6t = 30
-9j - 6t = -36

Answer 4

Once we add them, we'll get -4j = -6
Now we can find the value of j from this equation.

Answer 5

Now that we have a value for one variable which is j, we substitute this j = 1.5 into either equation 1 or 2. We can choose equation 2.

Answer 6

Now we have the value of t which is 3.75. Remember we named jelly beans as j and trail mix as t. The question wants the cost of jelly beans and the cost of trail mix.

Answer 7

So trail mix, t = $3.75 and jelly bean, j = $1.50. Therefore the cost of each pound of jelly bean is $1.50 and the cost of each pound of trail mix is $3.75.

Answer 8

I hope this explanation helps you to understand the question better.