Assign x to adult tickets and y to student tickets, then set up the system
5x+y=2465 and
x+y=1077
You can subtract the second equation from the first to get
4x=1388
=> x=347
Then to find y do 1077-347 to find
y=730
Final answer:
347 adult tickets and 730 student tickets were sold.
Hope I helped :)
1/9 of total marbles = 1/9 × 36 = 4
so Alexis gave 4 marbles to Sara.
And so Alexis is left behind with 32 (36-4) marbles and so Sara have 4 marbles now
To solve this we are going to use formula for the future value of an ordinary annuity:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
![FV](https://tex.z-dn.net/?f=FV)
is the future value
![P](https://tex.z-dn.net/?f=P)
is the periodic payment
![r](https://tex.z-dn.net/?f=r)
is the interest rate in decimal form
![n](https://tex.z-dn.net/?f=n)
is the number of times the interest is compounded per year
![t](https://tex.z-dn.net/?f=t)
is the number of years
We know from our problem that the periodic payment is $50 and the number of years is 3, so
![P=50](https://tex.z-dn.net/?f=P%3D50)
and
![t=3](https://tex.z-dn.net/?f=t%3D3)
. To convert the interest rate to decimal form, we are going to divide the rate by 100%
![r= \frac{4}{100}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B4%7D%7B100%7D%20)
![r=0.04](https://tex.z-dn.net/?f=r%3D0.04)
Since the interest is compounded monthly, it is compounded 12 times per year; therefore,
![n=12](https://tex.z-dn.net/?f=n%3D12)
.
Lets replace the values in our formula:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]](https://tex.z-dn.net/?f=FV%3D50%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.04%7D%7B12%7D%20%29%5E%7B%2812%29%283%29%7D%20-1%7D%7B%20%5Cfrac%7B0.04%7D%7B12%7D%20%7D%20%5D)
![FV=1909.08](https://tex.z-dn.net/?f=FV%3D1909.08)
We can conclude that after 3 years you will have $1909.08 in your account.