SOLUTION: Hello, I am studying for a test and I can’t figure out how to solve this: Danny needs to send 4 packages of different weights. The cost of the stamps depends on the weight of th

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Question 1021671: Hello, I am studying for a test and I can’t figure out how to solve this:
Danny needs to send 4 packages of different weights. The cost of the stamps depends on the weight of the package. The most expensive stamp costs 3 times more than the cheapest stamp. All together he paid 120 dollars. How much is the cheapest stamp and how much is the most expensive?

We are learning an = a1+d(n-1)
Answer is 15 and 45
Thanks!

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B4%5D=3a%5B1%5D
a%5B4%5D=a%5B1%5D%2B3d
So then,
3a%5B1%5D=a%5B1%5D%2B3d
2a%5B1%5D=3d
d=%282%2F3%29a%5B1%5D
You also know,
a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2Ba%5B4%5D=120
a%5B1%5D%2B%28a%5B1%5D%2Bd%29%2B%28a%5B1%5D%2B2d%29%2B%28a%5B1%5D%2B3d%29=120
4a%5B1%5D%2B6d=120
Substituting,
4a%5B1%5D%2B6%282%2F3%29a%5B1%5D=120
4a%5B1%5D%2B4a%5B1%5D=120
8a%5B1%5D=120
a%5B1%5D=120%2F8
a%5B1%5D=15
a%5B4%5D=3%2815%29=45