Any math lovers out there, can you help me????

Question

An ounce of dry-roasted cashew nuts (salted) contains 169 calories. There are 5 more grams of carbs than of protein. The total weight of protein, fat, and carbs is 26 grams. Protein and carbs have 4 calories per gram; fat has 9 calories per gram. How many grams of eah of protein, fat, and carbs are there? (Set up a system of equations and solve.)

I have no clue how to do this, and I've been working at it, but it doesn't make sense. Help??

Answer 1

Ok, lets use C, P and F to denote total grams of carbs, protein, and fat in an ounce of cashew.
carbs = C, protein = P, fat = F
Since There are 5 more grams of carbs than of protein:

C - 5 = P

The total weight of protein, fat, and carbs is 26 grams.

C+P+F = 26

Protein and carbs have 4 calories per gram; fat has 9 calories per gram. An ounce of dry-roasted cashew nuts (salted) contains 169 calories.

So

4C + 4P + 9F = 169

there is your system of equations.

Since C = P + 5, we can use subsitution on the other two equations:

(P+5)+P+F = 26 -> 2P + F + 5 = 26 -> 2P + F = 21
4(P+5) + 4P + 9F = 169 - > 8P + 9F + 20 = 169 -> 8P+9F = 149

So F = 21 - 2P

8P + 9 (21 - 2P) = 149
8P + 189 - 18P = 149
- 10P = -40
P = 4

Since 2P + F = 21 -> 8+F= 21 -> F=13

C - 5 = P -> C - 5 = 4 -> C= 9

So P=4 F=13 and C=9
Let's check:

C + P + F = 26 -> 4 + 13 + 9 = 26
4C + 4P + 9F = 169 -> 4*9 + 4*4+9*13 = 36 + 16 + 117 = 169

so there you go.

Answer 2

Let's try this....

Let's say
P = Protein in grams
C = Carb in grams
F = Fat in grams

The total weight of protein, fat, and carbs is 26 grams
P + C + F = 26

There are 5 more grams of carbs than of protein
P + 5 = C (think about this one carefully)

Protein and carbs have 4 calories per gram; fat has 9 calories per gram
4P + 4C + 9F = 169

Now, you have 3 equations. Let's call it equation 1, 2, and 3 (in order)

You substitute equation 2 into equation 1 and get:
P + F+ (P+5) = 26
P + F + P + 5 = 26
2P + F = 21 --- equation 4

You substitute equation 2 into equation 3 and get:
4P + 4(P+5) + 9F = 169
4P + 4P + 20 + 9F = 169
8P + 9F = 149 ---equation 5

Now, you have two equations involving just P and F. (system of equations)
Solve this system of equations between equation 4 and 5
Solve it and you get
F = 13
P = 4

Now you know F and P, you can arrive at C by using the first equation.
C = 9

What is strange about this problem is, the first part of the problem says AN OUNCE and the rest of the problem uses grams. An ounce is 31 grams.

This means there are 5 grams of absolutely nothing (does not contribute to calories). This was an assumption I had to go by, since you didn't say anything about it.