Answer:
Each pitcher has the same fraction of the other drink.
Step-by-step explanation:
After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).
The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.
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You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.
Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:
tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2
This problem is asking us to make an algebraic equation or representation of the situation. First we have to assign the variables which is already given in the problem. H is the number of the home team and V is the visiting team. Since the problem states there are the home team has five times as manyfans as the visiting team, then it can be represented as:
H = 5V
Also, H + V = 52,000. H and V can then be solves by solving the 2 equations simultaneously. The results are 43,333 and 8,667.
Y=8,4,2,-2 linear and in that order
Answer:
4x-12
Step-by-step explanation:
4 x x is 4x and 4x-3 is -12
