The equation y = 16x + 560 describes the number of calories in a recipe, where y is the total number of calories and x is the number of teaspoons of sugar added. The table shows the number of calories in another recipe, where y is the total number of calories and x is the number of teaspoons of honey added.

How many calories are in a teaspoon of sugar, and how many are in a teaspoon of honey?

Teaspoons of honey 1 2 4 7
Total calories 504 568 696 888

A teaspoon of sugar has calories.
A teaspoon of honey has calories.

Question

The equation y = 16x + 560 describes the number of calories in a recipe, where y is the total number of calories and x is the number of teaspoons of sugar added. The table shows the number of calories in another recipe, where y is the total number of calories and x is the number of teaspoons of honey added.
 
How many calories are in a teaspoon of sugar, and how many are in a teaspoon of honey?
 
Teaspoons of honey	1	2	4	7
Total calories	504	568	696	888
 
A teaspoon of sugar has   calories.
A teaspoon of honey has   calories.

anonymous · Answer

@sleepyjess

sleepyjess · Answer

Well, it gives you the calories for honey, and for sugar, I think you just substitute in 1 for x in the equation.

sleepyjess · Answer

Well, maybe, now I'm not sure after reading it again

anonymous · Answer

so how do i put in a equation

sleepyjess · Answer

Maybe @Directrix could help?

directrix · Answer

Let me think @sleepyjess   Sorry about that trig problem.

directrix · Answer

Did anybody get the equation for the data in the table?

sleepyjess · Answer

Let me work it out really quick

anonymous · Answer

it wants to know how many teaspoons of honey and sugar

anonymous · Answer

35 ?

directrix · Answer

@sleepyjess   What did you get for the calories/honey equation?

sleepyjess · Answer

I pmed it to you

anonymous · Answer

i got wrong thoe all they way i got 0%

anonymous · Answer

on my whole quiz

directrix · Answer

Does anybody agree with this for the calories/honey:

The equation of the line that passes through the points
(1,504) and (2,568)

is

y=64x+440

sleepyjess · Answer

@hartnn

sleepyjess · Answer

I came up with the same equation @Directrix

directrix · Answer

y = 16x + 560    calories/sugar

y=64x+440         calories/honey

hartnn · Answer

a teaspoon of honey= 1 teaspoon of honey = 504 cal

hartnn · Answer

a teaspoon of sugar  = 1 teaspoon of sugar = 560+16 = 576 cal

sleepyjess · Answer

I wasn't sure about the calories of sugar though because it says "y is the total number of calories and x is the number of teaspoons of sugar added." not y is the calories of sugar

hartnn · Answer

x teaspoon = y calories

sleepyjess · Answer

That is what I was originally thinking, but then I started to question myself :/

hartnn · Answer

y = 16x + 560    calories

y=64x+440         calories

are correct

directrix · Answer

The intersection is (5/2, 600) which I am now confused over the meaning of it.

directrix · Answer

x is the number of teaspoons, y the calories.

5/2 teaspoons of either sweetener produce the same calories.

But, that is not the question.

hartnn · Answer

why is intersection requireD?

a teaspoon of honey= 1 teaspoon of honey = 504 cal
a teaspoon of sugar  = 1 teaspoon of sugar = 560+16 = 576 cal

thats it!

directrix · Answer

Alrighty, then. I need to cogitate on this.  Thanks, @hartnn

directrix · Answer

And, thanks @sleepyjess  and @Lolafire

girlgoyleh. · Answer

the answer was, 16 calories of sugar
64 calories of honey

sleepyjess · Answer

this was a month ago.... -_-