Anita buys 6 large beads and 20 small beads to make necklace

[valymom]

I have 2 problems I am trying to solve:
Anita buys 6 large beads and 20 small beads to make a necklace. Ivan buys 4 large and 25 small beads for his necklace. Jill selects 8 large and 16 small beads to make an ankle bracelet. Without tax, Anita pays $2.70 and Ivan pays $2.85. How much will Jill pay?

(Equation 1) 6L + 20 S = 270
(Equation 2) 4L + 25S = 285
(Equation 3) 8L + 16S = J

a. What do the variables L, S, and J represent?
b. What are the units of L, S and J?
C. What does Equation 1 represent?

I have all the answers except what does J equal????? Please help if you can

 

[Loren]

Re: Help with Symbolic Representation Problems

One of the most important elements in solving word problems is to name things adequately and correctly. Don't say stuff like "L = large beads". Say, and write it down as part of your problem, "L represents the NUMBER of large beads" or "L represents the COST of one large bead" or whatever. Which one for this problem? And, be sure that every one of the variables is named. In your problem, note that two of the variables are of the same nature, whereas the third variable is of a different nature.

Eq. 1 along with eq. 2 represents 2 equations in 2 unknowns and as such is solvable. Solve for the two variables. Then plug those into eq. 3 to find the value of J.

 

[valymom]

Re: Help with Symbolic Representation Problems

Thanks for the info and I am understanding all that you said, but I am totally lost on figuring the equations, what do I do to what to solve???????

 

[skeeter]

Re: Help with Symbolic Representation Problems

(Equation 1) 6L + 20 S = 270
(Equation 2) 4L + 25S = 285

one method of solution (there are more) is called "elimination".
multiply (equation 1) by 2 and (equation 2) by -3, then add the two equations together term for term ...

12L + 40S = 540
-12L - 75S = -855
---------------------
-35S = -315 (note that the L's were "eliminated")
S = 9
each small bead costs 9 cents

go back to either of the two original equations, substitute 9 for S and determine the price of L, a large bead.

once you have L and S, you can ATQ.