Solving for Unknowns: Sandwich and Drink Order Equation - Try It Now!

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The discussion revolves around solving a mathematical problem involving sandwich and drink orders at a shop. Participants are tasked with completing a chart, writing equations, and determining the number of fruit drinks ordered based on a total bill of $17 for 20 items. The cost of sandwiches is $1.50 each, while fruit drinks are $0.40 each. Some participants emphasize the importance of attempting the problem independently to identify specific areas where help is needed. The conversation hints at the possibility of no valid solution existing for the equations set up from the given data.
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Who can solve this here

a. complete the chart for each problem
b. use the chart to write an equation
c. solve the equation and answer the question, explain if there is no solution

At a sandwich shop, sandwiches cost $1.50 each and fruit drinks $.40 each. If a bill for an order of 20 items was $17, how many fruit drinks were ordered.

Here's the chart

1.Number of each * 2.Value = 3.Total value
Fruit drinks: 1. x 2. .40 3.fill in the blank

Sandwiches: 1. fill in blank 2. 1.50 3.fill in the blank
 
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You were supposed to have read the guidelines when you registered for the forum! Thus, you should know that no one is going to do your homework for. That wouldn't help you or us. Try the problem your self so we will know what kind of help you need. (As far as I can see, there is no way to simply "write down" the information in the blanks. You will need to set up two equations and then solve the equations simultaneously to find the information you need.)
 
Hey I know I all ready turned it it and got it back i was just trying to see who all knew there wasn't a possible answer.
 
benifactorx said:
Hey I know I all ready turned it it and got it back i was just trying to see who all knew there wasn't a possible answer.
ok, we're not that stupid.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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