Answer:
Todd has 540540 songs in his playlist.
Vlad has 270270 songs in his playlist.
Becca has 162162 songs in her playlist.
Step-by-step explanation:
# of songs Todd has = T
# of songs Vlad has = V
# of songs Becca has = B
1) Todd has twice as many songs in his playlist as Vlad:
T=2V
2) Becca has three times as many songs in her playlist as Todd:
B=3T
3) All three people have a total of 243243 songs in their playlists:
T+V+B=243243
Because T=2V then you can substitute T as 2V in the second equation:
B=3(2V)
B=6V
Now in the final equation, you can substitute everything for V:
2V+V+6V=243243
9V=243243
V=27027
Now substitute for T:
T+1/2T+3T=243243
9/2T=243243
T=54054
Now substitute for B:
1/3B+1/6B+B=243243
3/2B=243243
B=162162
Check answers:
27027+54054+162162=243243
243243=243243
Look at the picture..............
Answer: $244.55
A = $250 ; r=0.002 t= 11 [From 2007 to 2018 , t=2018-2007]
Answer:
111 pieces of soda
Step-by-step explanation:
step 1
Find the area of the rectangular backyard
The area of the rectangular backyard is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
where
![L=18\frac{5}{6}\ yd=\frac{18*6+5}{6}=\frac{113}{6}\ yd](https://tex.z-dn.net/?f=L%3D18%5Cfrac%7B5%7D%7B6%7D%5C%20yd%3D%5Cfrac%7B18%2A6%2B5%7D%7B6%7D%3D%5Cfrac%7B113%7D%7B6%7D%5C%20yd)
![W=10\frac{2}{5}\ yd=\frac{10*5+2}{5}=\frac{52}{5}\ yd](https://tex.z-dn.net/?f=W%3D10%5Cfrac%7B2%7D%7B5%7D%5C%20yd%3D%5Cfrac%7B10%2A5%2B2%7D%7B5%7D%3D%5Cfrac%7B52%7D%7B5%7D%5C%20yd)
substitute
![A=(\frac{113}{6})(\frac{52}{5})](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B113%7D%7B6%7D%29%28%5Cfrac%7B52%7D%7B5%7D%29)
![A=\frac{5,876}{30}\ yd^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B5%2C876%7D%7B30%7D%5C%20yd%5E2)
step 2
Find the area of one piece of sod
The area of the rectangular piece of sod is
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
where
![L=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd](https://tex.z-dn.net/?f=L%3D1%5Cfrac%7B1%7D%7B3%7D%5C%20yd%3D%5Cfrac%7B1%2A3%2B1%7D%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%5C%20yd)
![W=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd](https://tex.z-dn.net/?f=W%3D1%5Cfrac%7B1%7D%7B3%7D%5C%20yd%3D%5Cfrac%7B1%2A3%2B1%7D%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%5C%20yd)
substitute
![A=(\frac{4}{3})^2\\\\A=\frac{16}{9}\ yd^2](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B4%7D%7B3%7D%29%5E2%5C%5C%5C%5CA%3D%5Cfrac%7B16%7D%7B9%7D%5C%20yd%5E2)
step 3
Find the pieces of sod needed
To find out how many whole pieces of sod will Jim need to buy to cover his backyard, divide the area of the backyard by the area of one piece of soda
so
![\frac{5,876}{30} : \frac{16}{9}=\frac{52,884}{480}=110.175](https://tex.z-dn.net/?f=%5Cfrac%7B5%2C876%7D%7B30%7D%20%3A%20%5Cfrac%7B16%7D%7B9%7D%3D%5Cfrac%7B52%2C884%7D%7B480%7D%3D110.175)
Round up
111 pieces of soda