Question

# A large juice jug holds the equivalent of 10 drinking cups: 4 jugs hold 189 ounces more than 13 drinking cups. How many ounces does a cup hold? Find the given, unknown, known, and solve

Answer

No valid solution

- Identify the given, unknown, and known:
- Let's assume that each cup holds X ounces.
- We can use the given information to create an equation: 4(10X + 189) = 13X.
- Distribute the 4 on the left side of the equation: 40X + 756 = 13X.
- Subtract 13X from both sides of the equation: 27X + 756 = 0.
- Subtract 756 from both sides of the equation: 27X = -756.
- Divide both sides by 27: X = -28.
- Since we cannot have negative ounces, our assumption was incorrect. We need to assume that each cup holds Y ounces more than 0oz.
- So, let's assume that each cup holds (X + Y) ounces, where Y > 0.
- We can use the given information to create an equation: 4(10(X+Y) + 189) = 13(X+Y).
- Distribute the 4 on the left side of the equation: 40X + 40Y + 756 = 13X + 13Y.
- Subtract 13X and 13Y from both sides of the equation: 27X + 27Y + 756 = 0.
- Subtract 756 from both sides of the equation: 27X + 27Y = -756.
- Divide both sides by 27: X + Y = -28.
- We know that Y > 0, so we can assume that Y = Z, where Z > 0.
- Substitute Z for Y in the equation from step 14: X + Z = -28.
- We've found an equation relating X and Z, but we don't know their specific values. We need another equation to solve for both variables.
- We use the given information: 10(X + Z) = 4(13).
- Simplify the right side of the equation: 10(X + Z) = 52.
- Divide both sides by 10: X + Z = 5.2.
- We now have two equations: X + Z = -28 and X + Z = 5.2. We can subtract equation 1 from equation 2 to eliminate Z.
- Subtract equation 1 from equation 2: 0X + 2Z = 33.2.
- Divide both sides by 2: Z = 16.6.
- Substitute Z for Y in the equation from step 14: X + 16.6 = -28.
- Subtract 16.6 from both sides of the equation: X = -44.6.
- We know that each cup holds (X + Y) ounces, so each cup holds (-44.6 + 16.6) = -28 ounces which is negative.
- Since we cannot have negative ounces, the problem does not have a valid solution. The given information is inconsistent.