Respuesta :
Answer:
The total weight of one die, one ball, and one marble is 75 grams.
Step-by-step explanation:
Consider the provided information.
Let d represents the number of dice, b represents the number of balls and m represents the number of marbles.
So according to the question.
The combined weight of 2 identical dice, 5 identical balls and 4 identical marbles was 260 grams.
[tex]2d+5b+4m=260[/tex] ....(1)
The combined weight of one die and one marble was 55 grams.
[tex]d+m=55[/tex]
[tex]m=55-d[/tex] ....(2)
3 balls weighed the same as two dice.
[tex]3b=2d[/tex]
Multiply both sides by 5 and divide by 3.
[tex]5b=\frac{10}{3}d[/tex] .....(3)
Now put the value of equation 2 and 3 in equation 1.
[tex]2d+\frac{10}{3}d+4(55-d)=260[/tex]
[tex]2d+\frac{10}{3}d+220-4d=260[/tex]
[tex]\frac{6d+10d-12d}{3}=40[/tex]
[tex]4d=120[/tex]
[tex]d=30[/tex]
Put d=30 in equation 2.
[tex]m=55-30[/tex]
[tex]m=25[/tex]
Put d=30 in equation 3.
[tex]5b=\frac{10}{3}\times 30[/tex]
[tex]5b=100[/tex]
[tex]b=20[/tex]
The total weight (in grams) of one die, one ball, and one marble is:
[tex]d+m+b=25+20+30[/tex]
[tex]d+m+b=75[/tex]
The total weight of one die, one ball, and one marble is 75 grams.
