mathstahp 3 years ago Need help with finding four numbers! (Problem in comments)

1. mathstahp

Suppose you have four numbers (call them a,b,c,d). They have the following characteristics: a is a perfect cube b is a perfect square c is divisible by 10 d is ONLY divisible by 5 They are also related in the following ways: \[c-a=4+b\] \[d/c = (a-(d-51)/a-(c-69))\] \[bc-ad = 2165\] \[-5(d-3a) = 80\] What is a, b, c, and d?

2. mathstahp

Oh, and just so it doesn't cause any confusion, the second equation can also be written as: \[d/c = (a-(d-51)\div(a-(c-69))\]

3. joshi

well i'm doing some calculations...but i think one thing i know is that d is 5?

4. mathstahp

how did you get d=5, joshi? I would just like to know how to start dealing with all of these.

5. joshi

oh wait never mind what i said about d. from c-a=4+b, i got c=4+b+a and i cross multiplied the second equation. and substituted c for 4+b+a that's what i have until now

6. mathstahp

Bahh...I'm just gonna give up on this stupid problem. Thanks for your help, though.

7. joshi

aw nooo well do you know the actual answer though? i'm going to finish this anyway, you're welcome