The Bradys and their maid, Alice, took a trip to Hawaii for their summer vacation. The travel agent told Ike that the trip would cost $210 for each child plus another $315 per adult. According to the credit card receipt the trip cost a total of $2205 for all 9 of them. Find the number of adults and children on the trip by writing a system of equations. PLEASE EXPLAIN HOW YOU GOT THE ANSWER. I HAVE ALOT OF QUESTIONS LIKE THIS ONE SO I NEED TO KNOW HOW YOU GOT THE ANSWER. THANK YOU!
2205 - (315 * 3) = ?
Divide the above answer by 210 to find the number of children.
or
number of children --- c
number of adults ---- a
a+c = 9
c = 9-a
210c + 315a = 2205
210(9-a) + 315a = 2205
1890 - 210a + 315a = 2205
105a = 315
a = 3
c= 6
3 adult and 6 children
check: 1+8 = 9
210(6) + 315(3) = 2205
Just realized I answered the same question over 2 years ago
http://www.jiskha.com/display.cgi?id=1421083338
Sure! To find the number of adults and children on the trip, we can set up a system of equations based on the given information.
Let's assume the number of adults on the trip is "a" and the number of children is "c".
According to the information given, the travel agent told Ike that the trip would cost $210 for each child and $315 per adult. Therefore, we can set up the first equation:
210c + 315a = 2205
This equation represents the total cost of the trip, where 210c represents the cost for each child and 315a represents the cost for each adult. The sum of these costs equals the total cost of $2205.
Now, we know that there were a total of 9 people on the trip, including both adults and children. So, the second equation is:
c + a = 9
This equation represents the total number of people on the trip, where c represents the number of children and a represents the number of adults. The sum of these numbers equals the total number of people, which is 9.
Now, we have a system of equations:
210c + 315a = 2205
c + a = 9
To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution to solve this system:
From the second equation, we can express c in terms of a:
c = 9 - a
Now, substitute this expression for c into the first equation:
210(9 - a) + 315a = 2205
Distribute 210:
1890 - 210a + 315a = 2205
Combine like terms:
105a = 315
Divide both sides by 105:
a = 3
Now, substitute the value of a into the second equation to find c:
c + 3 = 9
c = 6
Therefore, there were 3 adults and 6 children on the trip.
Hope this explanation helps! Let me know if you have any further questions.