Math Equation

Question

Maggie has two containers. The blue container can hold "b" cubic inches, and the red container can hold '"r" cubic inches. The blue container holds (4/3) of the amount the red container can hold. Maggie measures out 80 inches of sand by completely filling the blue container once and the red container twice.

What are the two system equations?
What is the volume, in cubic inches, of the red container?

Answer 1

So yeah, let's first translate this problem into symbols. "The blue container holds 4/3 of the amount the red container can hold" This means that b = (4/3)r since 4/3 of the amount the red container can hold is simply (4/3)r or 4r/3 since (4/3)r = (4/3) * (r/1) = (4 * r) / (3 * 1) = (4r/3) The other important part of this problem is: "Maggie measures out 80 [cubic] inches of sand by completely filling the blue container once and the red container twice." So filling the blue container once and the red container twice would be: b + 2r which the sentence tells us is equal to 80. Inches is not a proper measurement of sand. Let's assume they meant cubic inches. So b + 2r = 80 Now we have the system of equations: b = (4/3)r b + 2r = 80 we can substitute b for (4/3)r since we know they are equal from the first equation so we have: (4/3)r + 2r = 80 (4/3)r + (2/1)r = 80 (4/3)r + (6/3)r = 80 (this step might also help: r * ((4/3) + (6/3) = 80 and then r * ((4 + 6) / 3) = 80 (10/3)r = 80 (10/3)r * 1/10 = 80 * 1/10 (1/3)r = 8 (1/3)r * 3 = 8 * 3 r = 24 Which means the red container holds 24 cubic inches of sand. And since b = (4/3)r b = (4/3) * 24 b = 4 * (1/3) * 24 b = 4 * 8 b = 32 And the blue container holds 32 cubic inches of sand. Just to be complete. Hope that helps!

Answer 2

Here it is:

B = 4R/3

(4/3)R + 2R = 80

(4/3)R + (6/3)R = 80

(10/3)R = 80

10R = 240

R = 24 cubic inches.