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I need help with this math problem. Algebra 1?
inequality is 0.15t+0.10m=35
I need all of the possible combinations. so far I only have
0.15(30)+0.10(305)=35
and
0.15(0)+0.10(350)=35
you do not have to show work but it has to equal to 35 and use 0.15 and 0.10
and I'm sure I can do the next part which is finding 5 possible combinations of t and m that would keep it under 35 xD thank you.
1 Answer
- MathMan TGLv 77 years agoFavorite Answer
This is called a Diophantine Equation
if you want only integer solutions.
Otherwise it is a routine linear equation:
15 t + 10 m = 3500 (to get rid of fractions)
Divide by 5
3t + 2m = 700
m = (700 - 3t) / 2
Actually because of the small coefficients,
you can generate integer solutions easily.
Just need t to be even ...
t .... m
0 ... 350
2 ... 347
4 .... 344
... and so on
In general
t = 0 + 2x
m = 350 - 3x
for any integer (or non-integer for that matter) value of x.
x ... t ... m ... .15*t+.10*m
-10 ... -20 ... 380 ... 35
-9 ... -18 ... 377 ... 35
-8 ... -16 ... 374 ... 35
-7 ... -14 ... 371 ... 35
-6 ... -12 ... 368 ... 35
-5 ... -10 ... 365 ... 35
-4 ... -8 ... 362 ... 35
-3 ... -6 ... 359 ... 35
-2 ... -4 ... 356 ... 35
-1 ... -2 ... 353 ... 35
0 ... 0 ... 350 ... 35
1 ... 2 ... 347 ... 35
2 ... 4 ... 344 ... 35
3 ... 6 ... 341 ... 35
4 ... 8 ... 338 ... 35
5 ... 10 ... 335 ... 35
6 ... 12 ... 332 ... 35
7 ... 14 ... 329 ... 35
8 ... 16 ... 326 ... 35
