an apartment complex contains 200 apartments , of these , x are 3-room apartments, and the others are 4-room apartments . how ma
1 answer:
Answer:
Step-by-step explanation:
Let
x ----> 3-room apartments
200-x ----> 4-room apartments
we know that
To find out how many rooms are there in the complex, sum the number of 3-room apartments multiplied by 3 plus the number of 4-room apartments multiplied by 4
so
Apply distributive property
Combine like terms
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Call the amount of pineapple "P', and the amount of gingerale "G".
We know that a mix of pineapple and gingerale makes 200 cups. So:
We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
We can now solve by substitution:
For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]
We know that a mix of pineapple and gingerale makes 200 cups. So:
We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
We can now solve by substitution:
For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]
Answer:
Step-by-step explanation:
In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;
4, 8, 12, 16, 20...80
The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d
a is the first term = 4
d is the common difference = 21-8 = 8-4 = 4
n is the number of terms
On substituting, Tn = 4+(n-1)4
Tn = 4+4n-4
Tn = 4n
The nth term of the series is 4n.
Since the last term is 80, L = 4n
80 = 4n
n = 80/4
n = 20
This shows that the total number of terms in the sequence is 20
According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80 , we are to take the sum of the first 20terms of the sequence. Using summation notation;
4 + 8 + 12 + 16 + 20+ . . . + 80 =