Algebra question. How do you get the answer?

Question

Forty five packages were in a truck. some weighed 8 lb and the rest were 5 lb. If the total weight of all the packages was 186 lbs, how many of each type of package were on the truck?
Show work, please.

Answer 1

Yeah, even if the package were all of the lightest weight, the total would be 225 lbs.

Here's how it would break down in a spreadsheet.
8lb 5lb Weight
0 45 225
1 44 228
2 43 231
3 42 234
4 41 237
5 40 240
6 39 243
7 38 246
8 37 249
9 36 252
10 35 255
11 34 258
12 33 261
13 32 264
14 31 267
15 30 270
16 29 273
17 28 276
18 27 279
19 26 282
20 25 285
21 24 288
22 23 291
23 22 294
24 21 297
25 20 300
26 19 303
27 18 306
28 17 309
29 16 312
30 15 315
31 14 318
32 13 321
33 12 324
34 11 327
35 10 330
36 9 333
37 8 336
38 7 339
39 6 342
40 5 345
41 4 348
42 3 351
43 2 354
44 1 357
45 0 360

Answer 2

8 lb packages = x
5 lb packages = y

total packages:
x + y = 45
total weight:
8x + 5y = 186

Solve one equation for one variable;
x + y = 45
x = 45 - y

Now put that in the second equation:
8x + 5y = 186
8(45-y) + 5y = 186
360 - 8y + 5y = 186
360 - 3y = 186
-3y = -174
y = 58

NOTE: We have a problem... y = 58 can't be true because we only have 45 packages. (Did you type the problem correctly above?)

Anyway, assuming y=58 is correct:
Now put that back in the first equation to get x:
x = 45 - y
x = 45 - 58 = -13

Answer 3

let x be the packages that weigh 5-lb
let y be the packages that wigh 8-lb

there are 45 pacakages total
x+y = 45

the total weigh is 186lb, that means
5x+8y = 186


solve for x
x= 45-y

5(45-y) + 8y = 186
225 - 5y + 8y = 186
13y = -39

huhm.....the answer can't be negative. did you type the problem correctly?

Answer 4

You question has an error. If 45 five-pound packages were on the truck, they would weigh more than 186lbs!!