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m_a_m_a [10]
3 years ago
9

Alaina needs to sell 225 boxes in order to be the top seller. She sells thin mints and samoas to all of her customers for a tota

l of $628.00 in sales. The thin mints sell for $3.00 each and the samoas sell for $2.50 each. Which system of equations below could be used to find how many boxes of thin mints and samoas were sold?
Mathematics
1 answer:
Digiron [165]3 years ago
4 0

Answer:

94 boxes of samoas

131 boxes of thin mints

Step-by-step explanation:

m=mints

s=samoas

s+m=225    m=225-s

s(2.5)+m(3)=628

2.5s+3m=628

substitute for m

2.5s+3(225-s)=628

2.5s+675-3s=628

reduce

-0.5s=-47

s=94

m=131

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\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
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\end{array}\\ \quad \\


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\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
&&y=\cfrac{{{  k}}}{x}
\end{array}


now, we know that V varies directly to T and inversely to P simultaneously
thus\bf V=T\cdot \cfrac{k}{P}

so     \bf V=T\cdot \cfrac{k}{P}\qquad 
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\\\\\\
V=\cfrac{4T}{P}\qquad now\quad 
\begin{cases}
V=74\\
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