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# Algebra

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These are the fees for sending a package by Media Mail: 2.41 for the first pound, 0.41 per additional pound for the next six pounds 0.39 per additional pound after that. For example, a two-pound package costs 2.82 to send by Media Mail. If a package full of books costs 9.94, to send by Media Mail, how many pounds does the package weigh?

Apr 2, 2021

#1
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Because \$9.94>2.41+6(0.41)=4.87\$, we will need to use all the different options. That means that 9.94 can be written as 1(2.41)(first pound)+6(0.41)(for the additional 6 pounds)+k(0.39)(for the rest of the weight. Setting this equation equal to 9.94 gives:

\$1(2.41)+6(0.41)+k(0.39)=9.94\$

\$4.87+0.39k=9.94\$

\$0.39k=5.07\$

\$k=13\$

We're not quite done yet! k was only the number of pounds needed in the third option. We still need to take k and add in the 7 pounds that were the first and second options. So our final answer is:

\$k+7=(13)+7=\boxed{20}\$

Apr 2, 2021

#1
+484
+1

Because \$9.94>2.41+6(0.41)=4.87\$, we will need to use all the different options. That means that 9.94 can be written as 1(2.41)(first pound)+6(0.41)(for the additional 6 pounds)+k(0.39)(for the rest of the weight. Setting this equation equal to 9.94 gives:

\$1(2.41)+6(0.41)+k(0.39)=9.94\$

\$4.87+0.39k=9.94\$

\$0.39k=5.07\$

\$k=13\$

We're not quite done yet! k was only the number of pounds needed in the third option. We still need to take k and add in the 7 pounds that were the first and second options. So our final answer is:

\$k+7=(13)+7=\boxed{20}\$

RiemannIntegralzzz Apr 2, 2021
#2
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Very nice solution , Riemann   !!!!

CPhill  Apr 2, 2021
#3
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Thank you @CPhill!

RiemannIntegralzzz  Apr 2, 2021