# A box contains 1085 grams total weight of marbles and ball bearings There are two marbles for every three ball bearings. If each marble weighs 2.0 grams and each ball bearing weighs 9.0 grams, how many marbles are in the box?

70

This combination's (set's) unit weight is:

Since there are two marbles in each set, there are a total of:

By signing up, you agree to our Terms of Service and Privacy Policy

Let the number of marbles be ( M ) and the number of ball bearings be ( B ).

Given that the total weight of marbles and ball bearings is 1085 grams, we can write the equation: [ 2M + 9B = 1085 ]

Also, it is given that there are two marbles for every three ball bearings, so we have the ratio: [ \frac{M}{B} = \frac{2}{3} ]

We can solve this system of equations to find the value of ( M ), the number of marbles in the box.

First, we can rewrite the ratio equation as: [ M = \frac{2}{3}B ]

Now, substitute this expression for ( M ) into the first equation: [ 2 \left(\frac{2}{3}B\right) + 9B = 1085 ]

[ \frac{4}{3}B + 9B = 1085 ]

[ \frac{4}{3}B + \frac{27}{3}B = 1085 ]

[ \frac{31}{3}B = 1085 ]

[ B = \frac{1085 \times 3}{31} ]

[ B = 105 ]

Now, substitute the value of ( B ) back into the equation for ( M ): [ M = \frac{2}{3} \times 105 ]

[ M = 70 ]

Therefore, there are 70 marbles in the box.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The sum of two consecutive integers is −13. What are the numbers?
- The perimeter of a triangle is 7a - 11b. If two of its sides are 2a + b and a - 9b, what is the third side?
- How do you find Domain of the function #F (X) = 4x^2 - 5x + 10#?
- How do you simplify #29c + (-29c)#?
- How do you evaluate #6-3(2x+4)# when x=5?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7