Question

The combined weight of 2 identical dice, 5 identical balls and 4 identical marbles was 260 grams. The combined weight of one die and one marble was 55 grams. And 3 balls weighed the same as two dice. What was the total weight (in grams) of one die, one ball, and one marble?

Answer 1

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.

$2d+5b+4m=260$  ....(1)

The combined weight of one die and one marble was 55 grams.

$d+m=55$

$m=55-d$  ....(2)

3 balls weighed the same as two dice.

$3b=2d$

Multiply both sides by 5 and divide by 3.

$5b=\frac{10}{3}d$  .....(3)

Now put the value of equation 2 and 3 in equation 1.

$2d+\frac{10}{3}d+4(55-d)=260$

$2d+\frac{10}{3}d+220-4d=260$

$\frac{6d+10d-12d}{3}=40$

$4d=120$

$d=30$

Put d=30 in equation 2.

$m=55-30$

$m=25$

Put d=30 in equation 3.

$5b=\frac{10}{3}\times 30$

$5b=100$

$b=20$

The total weight (in grams) of one die, one ball, and one marble is:

$d+m+b=25+20+30$

$d+m+b=75$

The total weight of one die, one ball, and one marble is 75 grams.