Question

# Seneca and Artie are lab partners in science class. Today they have to weigh liquid. They...

Seneca and Artie are lab partners in science class. Today they have to weigh liquid. They have a try of 80 weights that they can use. There are four different kinds of weights: 50 grams, 25 grams, 15 grams, and 5 grams. The first liquid weights 85 grams. How many different combinations of weights will balance the scale for the first liquid ? Can you please draw a table to show all the possible combinations ?

19 ways

all the possible solutions= go through all the possible combinations.

So:
50+50=100, so you can only ever use one 50g weight. Not possible.

Using 50 ,25,15,5 = 4 ways

50+25+5+5

50+15+5+5+5+5

50+15+15+5.
50+5+5+5+5+5+5+5.

Using 25,15,5 = 9 ways

25+25+25+5+5
25+25+15+15+5
25+25+15+5+5+5+5
25+25+5+5+5+5+5+5+5
25+15+15+15+15=85
25+15+15+15=70+5+5+5=85
25+15+15=65+5+5+5+5+5+5=85
25+15=40+5+5+5+5+5+5+5+5+5=85
25+5+5+5+5+5+5+5+5+5+5+5+5

using 15& 5 = 5 ways

15+15+15+15+15+5+5
15+15+15+15+5+5+5+5+5
15+15+15+5+5+5+5+5+5+5+5
15+15+5+5+5+5+5+5+5+5+5+5+5
15+5+5+5+5+5+5+5+5+5+5+5+5+5+5

just 5g: 1 way
5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5

So total= 4+9+5+1 =19 ways