Finding the cost for each pound of jelly beans and each pound of almonds

Question

A store is having a sale on jelly beans and almonds. For 2 lbs of jelly beans and 6 lbs of almonds the total cost is $24. For 5 lbs of jelly beans and 3 lbs of almonds the total cost is $21. Find the cost for each pound of jelly beans and each pound of almonds

Answer 1

To solve for this, we need to write two equations with two variables, then use elimination or substitution to solve for each variable (this process is usually called "system of equations"). Let's call pounds of jelly beans "j" and pounds of almonds "a."

Now we need to write equations based on the information provided:

2j + 6a = 24

5j + 3a = 21

In order to eliminate one of the variables, we're going to subtract the second equation (5j + 3a = 21) from the first equation (2j + 6a = 24)--but first one of the variables need to have the same coefficient (the number in front of the variable). Let's look at "a." If we multiply the entire second equation by 2, then both equations have 6a:

2j + 6a = 24

10j + 6a = 42

Now, let's subtract the entire second equation from the first equation. Remember, we can only combine like terms:

2j + 6a = 24

-(10j + 6a = 42)

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-8j + 0a = -18

-8j = -18

j = -18/-8

j = 9/4

...or j = 2.25 (so the cost per pound of jelly beans is $2.25).

Substitute this answer back into either equation to solve for "a":

2j + 6a = 24

2(2.25) + 6a = 24

4.5 + 6a = 24

6a = 19.5

a = 3.25 (so the cost per pound of almonds is $3.25).

Of course, you can always check your work by substituting the values back into the equation (2.25 for j, and 3.25 for a) and see if they work!

I hope this helps!