Harrison has a total of 30 red and green bowling balls at his bowling alley. Each red ball weighs 8lbs and each green ball weights 9 lbs. If the total mass of green balls is 49 lbs heavier than the total mass of red balls, how many red balls does he have.
r + g =30
That first equation gives you to total number of balls.
This next equation is the number of balls times the weight of each ball. Taking into consideration that the green balls are 49 lbs heavier than the total mass of red balls.
9g = 49 + 8r
r + g = 30 or g = 30-r
you can replace g with its equivalent
9(30-r) = 49 + 8r
Now, just solve for r and you will have the number of red balls. You should check your work by finding the number of green balls. Check those values in the second equation to make sure you are correct.
To solve this problem, we need to set up equations based on the given information.
Let's assume the number of red balls is 'x'. According to the problem, there are a total of 30 balls, so the number of green balls would be '30 - x'.
The weight of each red ball is 8 lbs, so the total weight of all the red balls would be '8 * x' lbs.
Similarly, the weight of each green ball is 9 lbs, so the total weight of all the green balls would be '9 * (30 - x)' lbs.
According to the problem, the total weight of the green balls is 49 lbs more than the total weight of the red balls. So we can set up the following equation:
9 * (30 - x) = 8 * x + 49
Now, let's solve this equation to find the value of 'x':
9 * 30 - 9 * x = 8 * x + 49
270 - 9x = 8x + 49
270 - 49 = 8x + 9x
221 = 17x
x = 13
Therefore, Harrison has 13 red bowling balls.