The weight of raw coffee is [tex]\boxed{{\mathbf{37}}{\mathbf{.5 lb}}}[/tex] if raw coffee loses [tex]12\%[/tex] of its weight when it is roasted.
Further explanation:
Given:
It is given that raw coffee loses [tex]12\%[/tex] of its weight when it is roasted.
Step by step explanation:
Step 1:
First we determine the expression for weight of roasted coffee.
Consider [tex]x{\text{ lb}}[/tex] as the weight of raw coffee.
Consider the percent of raw coffee is 100%.
It is given that 12% coffee loses its weight.
The percent of roasted coffee can be calculated as,
[tex]\begin{aligned}{\text{percent of roasted coffee}} &= \left( {100\% - 12\% } \right) \\&= 88\%\\\end{aligned}[/tex]
Therefore, the weight of roasted coffee can be expressed as,
[tex]88\% {\text{ of }}x[/tex]
Step 2:
Now we need to find the weight of raw coffee as per the requirement of the question.
It is given that the weight of the roasted coffee is [tex]33{\text{ lb}}[/tex].
The weight of roasted coffee can be expressed in the form of equation as,
[tex]88\% {\text{ of }}x = 33[/tex]
The weight of raw coffee can be calculated as,
[tex]\begin{aligned}88\% {\text{ of }}x &= 33\\\frac{{88}}{{100}} \times x &= 33\\x&= 33 \times \frac{{100}}{{88}}\\x&= 37.5{\text{ lb}}\\\end{aligned}[/tex]
Therefore, the weight of raw coffee is [tex]37.5{\text{ lb}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Percentage
Keywords: Percentage, weight, raw coffee, roasted coffee, loses, difference, product, expression, terms, plus, multiply, addition, numbers.
