MHB How many weights of each type are needed at a gym to total 3180 pounds?

[bergausstein]

A gym offers a variety of weights for use by its mem-bers. If there are 6 more 50-pound weights than 100-pound weights and three times as many 20-pound
weights as 50-pound weights, for a total of 3180
pounds, how many of each weight are there?

this is howi solved it,

let
$x=$ # of 100 pound weights
$x+6=$ # of 50 pound weights
$3(x+6)=$ # of 20 pound weights

my equation,

$x+x+6+3(x+6)=3180=2x+3x+24=3180=5x+24=3180$ and then $x=631.2$

there are 631.2 (100 pound weights), 637.2(50 pound weeights), and 1911.6 (20 pound weights)

but my answers didn't make sense. because it's not a whole number. i expect to get a whole number.

can you help me with this. thanks.

 

[MarkFL]

You are using the number of weights rather than the weight of each set in your equation. You want:

$$x(100\text{ lb})+(x+6)(50\text{ lb})+3(x+6)(20\text{ lb})=3180\text{ lb}$$