Math 7B. Pattering and Algebraic Reasoning. Spring25 Sample work

Question 8
During cooking, a chicken loses 10% of its weight due to water loss. In order to obtain 1,170 grams of cooked chicken, how many grams of uncooked chicken must be used?
Use the following proportion to solve the problem.
___/100 = ___ grams/ ___ grams
90, 100, 1170, x, or 10
In order to obtain 1,170 grams of cooked chicken, how many grams of uncooked chicken must be used?
1,053 grams
1,287 grams
1,300 grams
1,340 grams

1 answer

To solve the problem, we first need to understand the relationship between the weight of the uncooked chicken and the cooked chicken after it loses 10% of its weight.

Let \( x \) be the weight of the uncooked chicken. Since the chicken loses 10% of its weight, it retains 90% of its original weight after cooking. Therefore:

\[ \text{Weight of cooked chicken} = 0.9 \times x \]

We want the cooked weight to equal 1,170 grams:

\[ 0.9x = 1170 \]

To find \( x \), we can divide both sides by 0.9:

\[ x = \frac{1170}{0.9} \]

Calculating that gives:

\[ x = 1300 \]

Thus, you need 1,300 grams of uncooked chicken to obtain 1,170 grams of cooked chicken.

Now, let's see how we can use the proportion that you provided to confirm our solution:

You mentioned using the following proportion:

\[ \frac{90}{100} = \frac{1170}{x} \]

Cross-multiplying gives:

\[ 90x = 100 \times 1170 \]

This simplifies to:

\[ 90x = 117000 \]

Now, dividing both sides by 90 gives:

\[ x = \frac{117000}{90} = 1300 \]

The method confirms that 1,300 grams of uncooked chicken must be used. The correct answer is 1,300 grams.