Each -ounce serving of cheddar cheese and each -ounce serving of tuna provides about microgram of vitamin B12. If a total of micrograms of vitamin B12 are consumed from eating ounces of cheese and ounces of tuna, which equation best represents this situation?
Explanation
Understanding the problem:
- We need to figure out how much B12 comes from x ounces of cheese and y ounces of tuna
- The total B12 = 1.7 micrograms
Breaking it down:
For Cheese:
- We know: 3.0 ounces of cheese = 1 microgram of B12
- Question: How much B12 is in x ounces of cheese?
- Set up proportion: 3.0 oz → 1 mcg, so x oz → ? mcg
- Answer: x/3.0 micrograms (or 0.33x when simplified)
For Tuna:
- We know: 1.2 ounces of tuna = 1 microgram of B12
- Question: How much B12 is in y ounces of tuna?
- Set up proportion: 1.2 oz → 1 mcg, so y oz → ? mcg
- Answer: y/1.2 micrograms (or 0.83y when simplified)
Building the equation:
- B12 from cheese + B12 from tuna = Total B12
- (x/3.0) + (y/1.2) = 1.7
- Converting to decimals: 0.33x + 0.83y = 1.7
Answer: B
The key insight is that we divide the ounces consumed by the serving size to find how many "servings" we ate, and each serving gives 1 microgram.