A store is having a sale on jelly beans and almonds. For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $20. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $23. Find the cost for each pound of jelly beans and each pound of almonds.
Costforeachpoundofjellybeans:$

Costforeachpoundofalmonds:$

Question

A store is having a sale on jelly beans and almonds. For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $20. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $23. Find the cost for each pound of jelly beans and each pound of almonds.
Costforeachpoundofjellybeans:$
 
Costforeachpoundofalmonds:$

mathstudent55 · Answer

This problem can be solved with a system of equations.
Are you learning how to solve systems of equations?

anonymous · Answer

been a while cant quite remember how to do it

mathstudent55 · Answer

First, we need to write the two equations.
Then, we'll solve them.

anonymous · Answer

6x+2y=20
3x+5y=23
is that correct

mathstudent55 · Answer

We need to choose two variables. 
Since most of the time we are used to using x and y as variables, let's use x and y. 
Let x = the cost per pound of jelly beans. 
Let y = the cost per pound of almonds.

mathstudent55 · Answer

The first case we have is 
"For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $20."
If jelly beans cost x dollars per pound, and you buy 6 pounds, how much does it cost?

anonymous · Answer

6x+2y=20
3x+5y=23
is that correct

mathstudent55 · Answer

Yes, you are correct.
Now you have the two equations for our system of equations.
Now we need to solve the system of equations.

mathstudent55 · Answer

We can use the substitution method.
First, take the first equation you wrote, and divide the entire equation by 2.
What do you get?

mathstudent55 · Answer

6x + 2y = 20
Divide the entire equation by 2 to get:
3x + y = 10

Now we solve the equation for y:
y = 10 - 3x

Now we do the substitution step. Since y = 10 - 3x, where we see y in the second equation, we substitute y with 10 - 3x

3x + 5y = 23
3x + 5(10 - 3x) = 23

Simplify the parentheses with the distributive property:
3x + 50 - 15x = 23

Collect like terms on the left side:
-12x + 50 = 23

Subtract 50 from both sides:
-12x = -27

Divide both sides by -12:
x = 2.25

Now that we know x, substitute x in the first original equation to find y.
6x + 2y = 20
6(2.25) + 2y = 20
13.5 + 2y = 20
2y = 6.5
y = 3.25

The price of jelly beans is $2.25 per pound,
and the price of almonds is $3.25 per pound

mathstudent55 · Answer

I have to go.
Take your time to go over the solution.
If you have questions, just ask, and I'll try to answer when I get back.

anonymous · Answer

ty i am looking iver to make sure i got it.. i have 5 like this

mathstudent55 · Answer

yw

anonymous · Answer

Thanks for taking the time to explain this to me.. Your help got me a 100 on my final exam

mathstudent55 · Answer

Wow. That's great. Congratulations.