estimating intercepts help please

[cltiller]

I am trying to figure out how to do this problem..

A teaspoon of sugar contains 15 calories. A grape contains approximately 3.5 calories. Write an inequality to show the combinations of the two items that will provide an amount of calories less than or equal to the 160 calories found in a 12 fluid ounce can of cola. Estimate the intercepts. Will the origin be in the solution set?

So here is what I have done so far...

15a + 3.5b is less than or equal to 160

Let a be calories in a tsp. of sugar
Let b be calories in a grape

x-intercept 15a + 3.5b = 160
15a =160
a= 10.7
y-intercept 15(0) + 3.5b = 160
3.5b = 160
b = 45.7

I think I'm totally confused! Help

 

[LivingMath]

Your math is good, but your explanations of that math are a little shaky.

15a + 3.5b is less than or equal to 160

Let a be calories in a tsp. of sugar <-- the number of calories in a tsp. of sugar is 15, not a
Let b be calories in a grape <-- the number of calories in a grape is 3.5, not b

a is the number of teaspoons of sugar
b is the number of grapes

x-intercept 15a + 3.5b = 160 <-- How can you have an x-intercept when there is no x in the equation?
15a =160
a= 10.7
y-intercept 15(0) + 3.5b = 160 <-- How can you have a y-intercept when there is no y in the equation?
3.5b = 160
b = 45.7

You found the a-intercept to be 10.7 and the b-intercept to be 45.7. Can you tell what that means in relation to the problem?

The next step is probably to try making a graph showing the a- and b-axes, the line 15a + 3.5b = 160. Select a few points to figure out which areas are valid solutions to the inequality. Then you should be able to see the answer to the final question: "will the origin be in the solution set?"

 

[Deleted member 4993]

The origin would be a glass of fresh-cool water......

 

[BigGlenntheHeavy]

\(\displaystyle Let \ x \ = \ a \ teaspoon \ of \ sugar \ (15 \ calories).\)

\(\displaystyle Let \ y \ = \ a \ grape \ (3.5 \ calories)\)

\(\displaystyle Then \ 15x+3.5y \ \le \ 160\)

\(\displaystyle See \ graph, \ shaded \ area \ below.\)

[attachment=0:3fg5e2al]aaa.jpg[/attachment:3fg5e2al]

 

[cltiller]

Thanks so much, you guys really help a woman out!
And yes I agree a tall, cold glass of water...