find the mass of each cube. Story problem that I need help with.

Question

Box A contains 53 cubes and has a mass of 1760 grams. Box B contains 18 cubes and has a mass of 1620 grams. The mass of box A is the same as the mass of box B. Every cube has the same mass. Find the mass of each cube.

Answer 1

Let b = the mass of a box and c = the mass of a cube

 

Box A contains 53 cubes and has a mass of 1760 grams:  53c + b = 1760

 

Box B contains 18 cubes and has a mass of 1620 grams:  10c + b = 1620, so b = 1620 - 10c

 

Since b = 1620 - 10c, let's substitute 1620 - 10c in place of b in teh seond equation and solve for c:

53c + b = 1760

53c + 1620 - 10c = 1760

43c = 140

c = 3.256 grams

 

Now we can solve for b:

b = 1620 - 10c

b = 1620 - 32.56

b = 1587.44 grams

 

Check:

53c + b = 1760

53(3.256) + 1587.44 = 1760

1760.08 = 1760                                  [Checks within rounding error]  

 

10c + b = 1620

10(3.256) + 1587.44 = 1620

32.56 + 1587.44 = 1620

1620 = 1620                                      [Checks]

 

Answer 2

Hello, Christine! I am originally from the other side of Illinois in the 'burbs of Chicago.

 

Let's let x = the mass of each cube.

 

Box A's cubes have a total mass of 53x. The mass of the box alone is the mass of the box minus the mass of the cubes, or 1760 - 53x.

 

We do the same thing with box B.

 

The mass of the two boxes are the same! 1760 - 53x = 1620 - 18x

 

Solve for x for the mass of each cube.

 

Hope this helps!