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DIA [1.3K]
3 years ago
12

Along with the flowers, Samantha bought 4 packages of glass beads and 2 vases. The vases cost $3.59 each and the total sales tax

was $1.34. The total amount she paid was $28.50, including sales tax. Explain a strategy she could use to find the cost of 1 package of glass beads.<br />
Mathematics
1 answer:
zmey [24]3 years ago
4 0

Samantha can find the total of the vases then add that and the sales tax. Once she has added those numbers up, she should subtract that from the total cost of the items. Once Samantha has subtracted, she should divide the answer by 4 to get the cost of an individual bag of beads

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SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}

So we have the formula

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We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}

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