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?

Question

Abigail Allen · Accepted Answer

70

#("marbles")/("ball bearings")=m/b=2/3# This combination's (set's) unit weight is: #(2xx2grams)+(3xx9grams) = 31 grams# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The total count of this unit weight in all of the combined mass is: #1085-:31 = 35 sets# Since there are two marbles in each set, there are a total of: #35xx2 = 70#

Isaiah Anthony · Answer

undefined 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.