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A freight elevator has a capacity of just under 3,000 pounds . A group of movers wants to move a piano that weighs 900 pounds and several crates of electronic that weigh 300 pounds each Part A : Write an inequality that shows how many crates of electronics can go on the freight elevator with the piano . Part B : Solve the inequality from Part A to find how many crates of electronics can go on the freight elevator

Answer :

Freight elevator's capacity will be defined as c.

Pounds (weight) will be defined as w.

So we can say that:

c<3000w

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Piano will be defined as 900w.

Number of crates of electronics will be defined as n300w, as we don't know how many crates there are.

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So, with this information we can say that:

[tex]900w+n300w<3000w[/tex]

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Now let's find out how many crates (n) can go on that elevator with the piano...

[tex]900w+n300w<3000w\\ \\ n300w<3000w-900w\\ \\ n300w<2100w[/tex]

[tex]\\ \\ \frac { 1 }{ 300w } \cdot n300w<2100w\cdot \frac { 1 }{ 300w } \\ \\ n<\frac { 2100 }{ 300 } \cdot \frac { w }{ w } \\ \\ n<7[/tex]

The elevator won't be able to accommodate a piano and 7 crates of electronics but it will be able to accommodate a piano and 6 crates of electronics.
part A + B  if you subtract 3,000 - 900 ( piano ) = 2,100 then if you keep subtracting 300 ( 1 crate of electronics ) soon you will get down to 0 then you can count how many times you subtracted 300 which in my answer 6 crates will fit with the piano part A ( 3,000 - 900) - 300 until 0  because it's 6 crates it said it was just under 3,000 pounds not on the exact weight.

 

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