Algebra word problem?? please?

Question

Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.

If someone could start this for me, I would really appreciate it. Thank you. I have one more week left of my algebra course and am just trying to get it done as best as I can. I have had a really hard time with Algebra.

Answer 1

Algebra is just about putting everyday things, like Jake and Sally's purchases, into a mathematical form. They usually use x's and y's, but you can use any letters you want to (I used to use ?'s, to remind me that that was what I was trying to find out). Anyway, in this case, first ignore anything that doesn't matter. It doesn't matter who bought the things, does it? Anyone could have bought them and the price would still be the same, so ignore Jake and Sally. To make it short, call the chocolate bars "c" and the gum "g". That just saves you writing "chocolate bars" and "packets of gum" loads of times. Ok , first sentence goes down as 3c + 1g = 1.75 (the dollar sign doesn't matter either. Just remember to put it back on to the answer when you're finished). The second sentence becomes 2c + 4g = 2.00. Put one above the other:
3c + 1g = 1.75
2c + 4g = 2.00
and add them together to get:
5c + 5g = 3.75.
Can you see from that that if you divide the whole thing by 5, you would get 1c +1g = 0.75? (Remember, all that means is that 1 chocolate bar and 1 pack of gum would cost 75 cents).
Now that doesn't tell you how much either the chocolate or the gum costs; it could be 70 cents and 5 cents, or 60 cents and 15 cents, or lots of other things. So how to find out the right amounts? Well you now know more than you did at the beginning, so compare what you know now with what you were told in the question. If 1c+ 1g = 0.75, then 2c + 2g = 1.50, right?
What is the difference between that and 2c + 4g = 2.00? You should see that the only difference is an extra 2g and an extra 0.50. So 2g = 0.50. (Or 2 packs of gum costs 50 cents). So 1g = 0.25. You know that 1c + 1g = 0.75, so 1c must be.......0.50.

Hope that helps, and algebra is not there to scare you.

Answer 2

We'll call the chocolate bars C and the gum - G
So: 3 c + g = 1.75
2c + 4g = 2.00

Remember that whatever you do to one side you do to the other.
Starting with the 2c + 4 g = 2.00, divide everything by 2
You have 2/2 c + 4/2 g = 2/2
c + 2 g = 1

That's as far as I'll take you.

Answer 3

use substitution:

Let c=chocolate bars and g=gum
Sally:
3c + g = 1.75

Jake
2c + 4g = 2.00


Using sally's equation, get the g to one side..
3c + g = 1.75
-3c -3c
g= -3c + 1.75


Now, using sally's new equation, substitute it into Jake's equation where the g is...
2c + 4(-3c + 1.75) = 2.00

Now solve...
2c + 4(-3c + 1.75) = 2.00
2c -12c + 7 = 2.00
-10c = -5.00
(divide each side by -10 and you get...)
c=.50


So, the chocolate bars each cost 50 cents and the gum costs 25 cents. To get the cost of the gum, all you do is sub the cost of the chocolate bars into either one of Sally or Jake's equations (the original ones) and solve for g.

For example, if you used Sally's equation:
3c + g = 1.75
3(.50) + g = 1.75
1.50 + g = 1.75
(subtract 1.50 form each side and you get...)
g = .25

Good Luck! hope this helps!!! :)

Answer 4

Set it up as an equation:

3 choc. bars + 1 gum = $1.75 3x + y = 1.75
2 choc. bars + 4 gum = $2.00 2x + 4y = 2.00

Then solve the first equation for y. When you find out what y is (which will not be a whole number), plug it into the second equation, then you will find x.

Answer 5

The cost of the chocolate bars are $.50/each and the gum is $.25 each.

Answer 6

3x + 1y = 1.75
x= chocolate bars
y= packs of gum

2x + 4y = 2.00

First solve for x in each of the problem, then plug x in to the problem to find y, or vise versa. the answer to x and y should be the same

Answer 7

substituting x and y for chocolate and gum:

3x+ y = 1.75
2x+4y = 2.00
------------------


multiply the top equation by -4 in order to eliminate the y.

-12x-4y=-7.00
2x+4y= 2.00
----------------------
-10x =-5.00

-5.00/-10= .50


In original equation substitute .50 for x and solve for y

(3*.50) +Y = 1.75
1.50+ y = 1.75
y= 1.75 - 1.50
y = .25

Plug those number in the second equation and it works.

Answer 8

Let x = number of chocolate bars
Let y = number of packs of gum

So....

3x + y = 1.75
2x + 4y = 2.00

Answer 9

3x+y= 1.75
2x+4y= 2.00
5x+5y=3.75
x+y= 0.75

At this point, I guessed which numbers worked, but they have to work in both the original equations.
Chocolate bar is $.50, gum is $.25

Answer 10

50 cents and 25 cents

sorry just did it in my head.