5 green balls and 2 red balls together weigh 10 pounds, and 1 green ball and 4 red balls together weigh 7 pounds. If all red balls weigh the same amount and all green balls weigh the same, then what is the weight of 8 red and 8 green balls together?
I'm not sure at all how to solve this one, either... please help in any way you can! Thanks! :-)
Responses
algebra - Melanii, Tuesday, February 17, 2009 at 4:59pm
i kinda did ratios
5:2 =10
4:1 =7
8:8 =?
so then
2 1/2:1 =5
2:1/2 =3 1/2
4:4 =?
algebra - Chopsticks, Tuesday, February 17, 2009 at 5:00pm
The red ball weighs about 1.4
the green ball weighs about 1.44
So i think 8r and 8g ball weighs about 22.72
This is not an exact measurement of each balls, just an estimate.
algebra - Rachelle, Tuesday, February 17, 2009 at 5:03pm
Wow... 1/2 of a ball. :-)
I see what you were trying to get across... but our teacher never showed us a problem like this... so frustrating.
I don't know if your ratio way is exactly right, but it is a good way to straighten out the info.
Wait... I got something!
Maybe it's...
g is green and r is red.
5g + 2r = 10
g + 4r = 7
Then, if we add those together and find out what one ball weighs individually, then you just multiply it by 8! I think I got it! :-)
just reposting :):):)
algebra - Melanii, Tuesday, February 17, 2009 at 5:07pm
thanks chopsticks.
yeah that makes sense... i'm gonna try it.
those are all incorrect idiots
Haha, I love your enthusiasm, Rachelle! You're definitely onto something with your equations. Let's solve the system to find the weight of a green ball (g) and a red ball (r).
From the first equation:
5g + 2r = 10
From the second equation:
g + 4r = 7
To make things easier, let's solve the second equation for g:
g = 7 - 4r
Now we can substitute this value of g into the first equation:
5(7 - 4r) + 2r = 10
Simplifying this equation, we get:
35 - 20r + 2r = 10
-18r = -25
r = 25/18
Now we can substitute this value of r back into the second equation to find g:
g + 4(25/18) = 7
g = 7 - (100/18)
g = 49/18
So the weight of a red ball is approximately 25/18 pounds and the weight of a green ball is approximately 49/18 pounds.
Now, to find the weight of 8 red and 8 green balls together, we just multiply the weight of one red ball by 8 and the weight of one green ball by 8, and add them together:
(25/18)*8 + (49/18)*8
Doing the math, we get:
200/18 + 392/18
592/18
Approximately 32.9 pounds.
So the weight of 8 red and 8 green balls together is approximately 32.9 pounds. And remember, Rachelle, don't throw those balls around too much, you might end up with a weightlifting session instead!
To solve this problem, you can use a system of equations to find the weight of each ball individually, and then multiply that weight by 8 for both the red and green balls to find the weight of 8 red and 8 green balls together.
Let's assign variables to the weight of each ball. Let 'g' represent the weight of a green ball, and 'r' represent the weight of a red ball.
From the given information, we can create two equations:
Equation 1: 5g + 2r = 10
Equation 2: g + 4r = 7
To solve this system of equations, we can use the method of substitution or elimination. In this case, we can use elimination.
To eliminate 'g' from the equations, we can multiply Equation 2 by 5:
5(g + 4r) = 5(7)
5g + 20r = 35
Now we can subtract Equation 1 from this new equation:
(5g + 20r) - (5g + 2r) = 35 - 10
18r = 25
Divide both sides by 18:
r = 25/18
Now we have the weight of a red ball, which is approximately 1.39 pounds.
To find the weight of a green ball, we can substitute this value of r back into Equation 2:
g + 4(25/18) = 7
g + (100/18) = 7
g = 7 - (100/18)
g = (126-100)/18
g = 26/18
g = 1.44
So, the weight of each red ball is approximately 1.39 pounds, and the weight of each green ball is approximately 1.44 pounds.
To find the total weight of 8 red and 8 green balls together, we add the weights:
(8 * 1.39) + (8 * 1.44) = 27.92 pounds
Therefore, the weight of 8 red and 8 green balls together is approximately 27.92 pounds.