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Please help See attached photoWorking with system of linear problems not a quiz or homework knowledge check and at the bottom gives you explanation

Please Help See Attached PhotoWorking With System Of Linear Problems Not A Quiz Or Homework Knowledge Check And At The Bottom Gives You Explanation class=

Sagot :

Large boxes: L, 45 lb

Small boxes: S, 30 lb

There are 125 boxes, then:

[tex]L+S=125[/tex]

The total weight in boxes is 4575 lb:

[tex]\begin{gathered} 45L+30S=4575 \\ \Rightarrow\frac{45L}{15}+\frac{30S}{15}=\frac{4575}{15} \\ \Rightarrow3L+2S=305 \end{gathered}[/tex]

Then, the system of equations is:

[tex]\begin{cases}L+S=125\ldots(1) \\ 3L+2S=305\ldots(2)\end{cases}[/tex]

From (1), L = 125 - S, so we use this on (2):

[tex]\begin{gathered} 3(125-S)+2S=305 \\ 375-3S+2S=305 \\ S=70 \end{gathered}[/tex]

Using this result on (1):

[tex]\begin{gathered} L+70=125 \\ \Rightarrow L=55 \end{gathered}[/tex]

There are 55 large boxes and 70 small boxes

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