At a bagel shop, 2 coffees and 4 bagels cost $6.00. Two coffees and 7 bagels cost $8.25. What is the unit price of one coffee and the unit price of one bagel?
my answer:
1 bagel= $0.75
1 coffee= $1.00
Find the 5,550th term in the sequence 4 1/2, 5, 5 1/2, 6, 6 1/2?
my answer: 2779
the last one looks just like
http://www.jiskha.com/display.cgi?id=1459986016
but you changed the first term
so the answer is not 2779 like in your previous question
for the bagel question, which I did for you here
http://www.jiskha.com/display.cgi?id=1459985491
how did you get $1.00 for the coffee
I had b = 75
subbing that into
2c + 4b = 600
2c + 300 = 600
2c = 300
c = 150
so the coffee costs $1.50
To find the unit price of one coffee and one bagel, we can set up a system of equations using the given information.
Let's assume the unit price of a coffee is "c" dollars and the unit price of a bagel is "b" dollars.
From the first statement, we know that 2 coffees and 4 bagels cost $6.00, so we can write the equation: 2c + 4b = 6.
From the second statement, we know that 2 coffees and 7 bagels cost $8.25, so we can write the equation: 2c + 7b = 8.25.
To solve this system of equations, we can use either substitution or elimination method.
Using elimination method:
Multiply the first equation by 7 and the second equation by 4 to eliminate the variable "c".
14c + 28b = 42
8c + 28b = 33
Subtract the second equation from the first equation:
6c = 9
c = 9/6 = 1.50
Now substitute the value of c in any of the original equations to find the value of b.
2(1.50) + 7b = 8.25
3 + 7b = 8.25
7b = 8.25 - 3
7b = 5.25
b = 5.25/7 = 0.75
Therefore, the unit price of one coffee is $1.50 and the unit price of one bagel is $0.75.
For the second question, the given sequence is 4 1/2, 5, 5 1/2, 6, 6 1/2. This is an arithmetic sequence with a common difference of 1/2.
Using the formula for the nth term of an arithmetic sequence, we can find the 5,550th term:
nth term = first term + (n - 1) * common difference
In this case, the first term is 4 1/2, which can be written as 9/2.
The common difference is 1/2.
Plugging these values into the formula:
5550th term = 9/2 + (5550 - 1) * 1/2
= 9/2 + (5549) * 1/2
= 9/2 + 5549/2
= (9 + 5549)/2
= 5558/2
= 2779
So, the 5,550th term in the sequence is 2779.