Question

Sage is making roasted potatoes for a benefit dinner. The committee gives her money to buy 10 bags of potatoes.

Write an equation to help Sage determine how many servings of potatoes she can prepare.
Let's let
n = number of servings
p = grams of potatoes per serving
c = grams of potatoes in each bag

Help? :/ How do I do this?

@agent0smith

Answer 1

Well 10c (10 bags times c grams per bag) gives the total number of grams of potatoes she will have purchased.

np (number of servings times grams per serving) gives the total number of grams served to people

np can be at most 10c, so \[\Large np \le 10c\] or just np = 10c

Answer 2

\[n = \frac{ 10c }{ p }\]

Was the right answer ._.

Answer 3

@AllTehMaffs @Compassionate Can you explain how that answer is what it is? :/ I'm confused on it.. :l. All it gives is the answer, not the explanation.. >.<

Answer 4

np = 10c

the answer above comes from this...

Answer 5

divide both sides by p

Answer 6

Oh.. Sorry >.<

Answer 7

so let's reput units on everything, like agent0smith did in his first post.

\[
n = \ \textrm{ servings}
\\ \
\\ p = \ \textrm{grams of potato per serving} \ = \ \ \frac{\textrm{grams of potatoes}}{\textrm{serving}}
\\ \
\\ \
c= \ \textrm{grams of potatoes in a bag} = \ \ \frac{\textrm{grams of potatoes}}{\textrm{bag of potatoes}}\]
\[\textrm{We have} \ \ 10 \ \ \textrm{Bags of potatoes} \ \ \textrm{total}\]


\[np = 10 c\]
\[\small \ \ \Bigg(\frac{\textbf n \ \ servings}{1} \Bigg) \Bigg( \frac{\textbf p \ \ \textrm{grams of potatoes}}{\textrm{serving}} \Bigg) =

\Bigg( \frac{10 \cancel{ \textrm{Bags of potatoes}}}{1} \Bigg) \Bigg(\frac{\textbf c \ \ \textrm{grams of potatoes}}{\cancel{\textrm{bag of potatoes}}} \Bigg)\]

The units show that in order to get "servings" alone on the left, we have to divide 10c by p

\[\small \ \ \Bigg(\frac{\textbf n \ \ servings}{1} \Bigg) =

\Bigg( \frac{10 \textbf c \ \textrm{grams of potatoes}}{ \frac{\textbf p \ \ \textrm{grams of potatoes}}{\textrm{serving}}} \Bigg) \]

\[n \ \textrm{servings} = \frac{10 \ c}{p} \ \textrm{servings} \]