Question

Paula mixed 2 cups of sunflower seeds and 3 cups of raisins to make a snack for a hike. she figured that the mixture would provide her with 2900 calories of food energy. find the number of calories per cup of raisins if it is 400 less than the number of calories per cup of sunflower seeds.

Answer 1

Hi!

I would use system of equations to solve this.

Let r = calories per cup of raisins and s = calories per cups of sunflower seeds

I would set up the two equations as one being 2 cups of sunflowers + 3 cups of raisins = 2900 calories, and one cup of raisins + 400 calories = one cup of sunflower seeds. Those written out as equations are:

2s + 3r = 2900

r + 400 = s

Now, you can use substitution, substituting r + 400 into the first equation for s (as that equals s in the second equation) and you get:

2 (r + 400) + 3r = 2900

Now solve.

2r + 800 + 3r = 2900

5r = 2100

r = 420 calories

(For the check, for one cup of sunflower seeds, there are 820 calories, based off the fact raisins have 400 less calories than the sunflower seeds)

To check:

2 (820) + 3 (420) = 1640 + 1260 = 2900

420 + 400 = 820

So our answer of 420 calories is correct.

Hope this helped!