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! :-)
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 =?
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.
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! :-)
thanks chopsticks.
yeah that makes sense... i'm gonna try it.
Yes, Chopsticks, after trying the way I described in my last response, I got the same answers you have.
Thank you for your help! :-)
i reposted it btw ok? :):):) just so you know.
To solve this problem, we can use a system of equations. Let's assign variables to the weight of a green ball (let's call it G) and the weight of a red ball (let's call it R).
From the information given, we can set up two equations:
Equation 1: 5G + 2R = 10 (equation representing the weight of 5 green balls and 2 red balls)
Equation 2: 1G + 4R = 7 (equation representing the weight of 1 green ball and 4 red balls)
We now have a system of two equations with two variables. Our goal is to solve for G and R, so we can find the combined weight of 8 red and 8 green balls.
To eliminate one variable, we can multiply Equation 2 by 5 and Equation 1 by 7, so the coefficients of R are the same:
5G + 20R = 35 (multiply Equation 2 by 5)
35G + 14R = 70 (multiply Equation 1 by 7)
Subtracting these two equations will eliminate the R variable:
(35G + 14R) - (5G + 20R) = 70 - 35
35G + 14R - 5G - 20R = 35
30G - 6R = 35
Now we have a new equation:
Equation 3: 30G - 6R = 35
We can solve for G or R using this equation. Let's solve for G:
30G - 6R = 35
30G = 35 + 6R
G = (35 + 6R) / 30
G = (35/30) + (6R/30)
G = 7/6 + (R/5)
We have expressed G in terms of R. Now, we can substitute this equation into Equation 1 to solve for R.
5G + 2R = 10
5((7/6) + (R/5)) + 2R = 10
(35/6) + (5R/6) + 2R = 10
(35 + 5R + 12R) / 6 = 10
35 + 5R + 12R = 60
17R = 25
R = 25/17 ≈ 1.47
We have found the weight of one red ball, which is approximately 1.47 pounds.
Now, we need to find the weight of one green ball. We can substitute this value of R into Equation 2:
1G + 4R = 7
1G + 4(1.47) = 7
1G + 5.88 = 7
1G = 7 - 5.88
1G ≈ 1.12
We have found the weight of one green ball, which is approximately 1.12 pounds.
Finally, we can find the weight of 8 red and 8 green balls together:
Weight of 1 red ball = 1.47 pounds
Weight of 8 red balls = 8 × 1.47 = 11.76 pounds
Weight of 1 green ball = 1.12 pounds
Weight of 8 green balls = 8 × 1.12 = 8.96 pounds
Total weight of 8 red and 8 green balls together = 11.76 + 8.96 = 20.72 pounds
Therefore, the weight of 8 red and 8 green balls together is approximately 20.72 pounds.