find the fat content of meal a and of meal b.

Question

a nutritionist finds that meal a has more fat than meal b. meal a has 1 ​gram(s) more than six times the amount of fat that meal b has. the difference in the fat content between meal a and meal b is 36 grams. find the fat content of meal a and of meal b.

Answer 1

We use the information we know to build two formulas, which will allow us to solve for the two variables.

1. Our first piece of information translates to a > b
2. Our second piece of information translates to a = ​1 + 6*b
3. Our third piece of information tells us that |a-b| = 36
4. Combining 1 and 3 we know that because a>b, we can drop the absolute value above, so a - b = 36
5. Plugging in the first formula, which defines a into the second formula, we get:
6. (1 + 6*b) - b = 36
7. 1 +5*b = 36
8. 5*b = 35
9. b = 7
10. We can plug this value of b into the first formula to solve for a:
11. a = ​1 + 6*b
12. a = 1 + 6*7
13. a = 1+42
14. a = 43

Answer 2

a = 6b + 1 and a - b = 36

So, (6b+1) - b = 36

5b = 35

So, b = 7 g and a = 43 g