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:
start with using the 50g weight:
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
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