Respuesta :
Answer:
150c + 13,700 < 23,000
Step-by-step explanation:
Greatest weight that can be loaded into the container = 23,000 kilograms
Weight of each crate = 150 kilogram
Weight of other shipment = 13,700 kilograms
c = total number of 150-kilogram crates that can be loaded
This can be represented by the inequality:
150c + 13,700 < 23,000
That is, Weight of each crate multiplied by total number of 150-kilogram crates that can be loaded Plus Weight of other shipment less than greatest weight that can be loaded into the container
Answer:
c<62
Step-by-step explanation:
We know:
\color{blue}{\text{weight preloaded}}=
weight preloaded=
\,\,\color{blue}{13700}
13700
\color{red}{\text{weight per crate}}=
weight per crate=
\,\,\color{red}{150}
150
\color{purple}{\text{weight capacity}}=
weight capacity=
\,\,\color{purple}{23000}
23000
150
150
150
...
13700
23000
weight of all crates
Method 1 (Unwinding):
\color{green}{\text{weight of all crates}}=
weight of all crates=
\,\,\color{purple}{\text{weight capacity}}-\color{blue}{\text{weight preloaded}}
weight capacity−weight preloaded
=
=
\,\,\color{purple}{23000}-\color{blue}{13700}
23000−13700
=
=
\,\,\color{green}{9300}
9300
\text{number of crates}=
number of crates=
\,\,\frac{\color{green}{\text{weight of all crates}}}{\color{red}{\text{weight per crate}}}
weight per crate
weight of all crates
​
=
=
\,\,\frac{\color{green}{9300}}{\color{red}{150}}
150
9300
​
=
=
\,\,62
62
6262 is the number of crates that can be loaded into the shipping container for a total weight of 23000 kilograms. But the "greatest" weight means less than 23000 kilograms can also be loaded into the container, so fewer than 62 (61, 60, ...) crates can also be loaded.
c \leq62
c≤62
\leq≤ or "less than or equal to" means that exact amount or less
Method 2 (Algebra):
\text{\(c=\) number of crates}
c= number of crates
The greatest weight means less than 23000 kilograms can also be loaded into the container, so we will use the \leq≤ ("less than or equal to") symbol:
\color{red}{\text{weight per crate}}\cdot\text{\# of crates}+\color{blue}{\text{weight preloaded}}\leq\color{purple}{\text{weight capacity}}
weight per crate⋅# of crates+weight preloaded≤weight capacity
\color{red}{150}c+\color{blue}{13700}\leq
150c+13700≤
\,\,\color{purple}{23000}
23000
-\color{blue}{13700}\phantom{=}
−13700=
\,\,-\color{blue}{13700}
−13700
Subtract 13700 from both sides
\color{red}{150}c\leq
150c≤
\,\,9300
9300
\frac{\color{red}{150}c}{\color{red}{150}}\leq
150
150c
​
≤
\,\,\frac{9300}{\color{red}{150}}
150
9300
​
Divide both sides by 150
c\leq
c≤
\,\,62
62
