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

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

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=(10)/(3)d` .....(3)

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

`2d+(10)/(3)d+4(55-d)=260`

`2d+(10)/(3)d+220-4d=260`

`(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=(10)/(3)* 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.