There are some red balls and green balls. If the number of red balls is greater than the number of green balls by 22, AND the total number of balls is 50, what is the number of red balls ONLY?

Question

Doing this for a math equation. (Note - The answer to this problem is actually 36, but I only want to find out the equation/step by step calculations on this one so...)

Answer 1

Hello, there are a couple of ways to set this up. I don't know what level your at and I cant make any assumptions about what you know. This may be lengthy and more than what your asking but I just want to make sure you understand so that it's easier for you to do on your own in the future so just bear with me.

Let letter R represent the # of red balls and

Let letter G represent the # of green balls

R= Red, G =Green

The word problem is telling you there are 22 more red balls than there are green. So(for example) if there were 1 green ball, then there would be( 1+ 22) or 23 red balls. So we translate it with this equation:

Red = Green + 22(rewrite as R=G+22)

and we know the following information

Red + Green = 50 (rewrite as R+G=50)

So to solve this we basically have to combine the two equations using a substitution method

Equation 1: R + G = 50

Equation 2: R= G +22

By plugging the second equation into the first, we can find the number of green marbles first

Replace the R in the first equation with (G+22)

R + G = 50

(G+22) + G = 50

2G + 22 = 50

- 22 -22( subtract 22 from both sides)

2G = 28(divide both sides by 2)

G=14

So now that we found that there are 14 green, just plug it into either equation to find out how many red there

are. It's easier to just use equation 2

Equation 2: R = G+22

R = 14+22

R= 36

Now you were only asked to solve for red and this was lengthy but there may be times when your asked for the number of Green also or both so now you know how to solve for both if you need to.

Answer 2

Since you are looking for the number of red balls, introduce a variable, R to indicate the number of Red balls and G to indicate the number of Green balls. You are also given that all the balls are Red or Green and the total number of balls is 50. You are also told that the number of Red balls is 22 greater than the number of Green balls.

So you can write two equations:

(1) R + G = 50 ; total of 50 balls

(2) G = R - 22 : 22 more Red than Green

You now realize R and G are dependent variables and you wisely decide to replace G with R-22 in equation (1) and solve for R since that is what the problem is asking for.

Equation (1) becomes

(1') R + R - 22 = 50

Simplify

(1'') 2 R - 22 = 50

2 R = 72

R = 72/2 = 36

If you were asked for the number of Green balls, you would solve G = R-22 = 36-22 = 14.

You can check your answer: R + G = 36 +14 = 36 +14 = 50