Question

A candy store makes a 6–pound mixture of gummy bears, jelly beans, and gobstoppers. The cost of gummy bears is $1.00 per pound, jelly beans cost $3.00 per pound, and gobstoppers cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $8.00. How much of each ingredient did the store use?

Answer 1

Could you be more specific, @ericaneal1 ?

Answer 2

ok 3 times 1 is 3 there you go keep doing that then add if you dont get the divideing way

Answer 3

That sounds like it would take a really long time.
I would recommend algebra. There are three unknowns, so you need three equations. Do you see the three separate pieces of information, @jacobblocker ?

Answer 4

yes

Answer 5

The first thing you want to do (after reading the problem twice to understand the question being asked, and to gather the necessary information), is to define your variables.
I would do something like G = pounds of gummy bears, J = pounds of jelly beans, S = pounds of gobstoppers.

Answer 6

Using those variables, set up an equation for each sentence in the word problem.

Answer 7

is it something like this

g+j+s=8
g=3j
1g+1j+3s=6

Answer 8

Hmm, pretty close. The first statement is about weight, and the weight was 6 pounds, not 8.
In the third statement, it is the jelly beans that cost 3 $/Lb. not the gobstoppers, and the total cost is 8, not 6$

Answer 9

You got the right idea though. :-)

Answer 10

good

Answer 11

So, ultimately you want to get down to one equation with one unknown in it, so you can solve for its value. Right now you have three equations, so you'll first want to combine those in a way to make two equations with two unknowns, then do some substitution to combine those into a single equation.

My first hint is to substitute the G = 3J expression into the other two equations, then use those to solve for J and S.

Answer 12

ill try to

Answer 13

Yeah, keep playing around with it, and let me know how far you get.
I'll work on it too and see if I can find a solution.

Answer 14

im lost

Answer 15

What do you have so far?

Answer 16

i dont know how to eliminate the equations

Answer 17

Did you make this substitution?
\[\large G=(3J).\]
\[\large (G)+J+S=6 \rightarrow (3J)+J+S=6.\]
\[\large (G)+3J+S=8 \rightarrow (3J)+3J+S=8.\]

Answer 18

no

Answer 19

Do that first; it'll make your life a lot easier.

Answer 20

well you need to do that first

Answer 21

You'll have two equations in J and S; you can solve the first one for S in terms of J and substitute that into the second one to get a value for J, then it's back-substitution to find the remaining values.

Answer 22

A solution using Mathematica's Minimize function is attached.